John S. Wilkins has put up a survey What does "Darwinism" mean? at Evolving Thoughts. I thought I could complement this by delving into some archives and lifting historical quotes pertinent to the question. Below are historical quotes defining the term Darwinism by Thomas Huxley (1860), Carl Nägeli (1865), Ernst Haeckel (1866), Charles Hodge (1874), Samuel Butler (1880), Alfred Wallace (1889), George Romanes (1889), August Weismann (1893), Liberty Bailey (1894), George Romanes (1897), Petr Kropotkin (1902), Vernon Kellogg (1907), Thomas Morgan (1909), Richard Lewontin (1981) and George Williams (1992).
Although I expected the usual disunity about terms and meanings, the researchers were surprisingly d'accord that Darwinism means explaining adaptation through natural selection. So far, theologian Hodge has been the only dissenter believing that Darwinism was truly about atheism.
The dissent among scientists only began with the question whether natural selection was the main or sole mechanism of evolution. The context of this dispute was intricate. Wallace denied other factors of evolution besides natural selection, such as sexual selection or the inheritance of acquired trait variations. In this respect he was more extreme than Darwin. Weismann joined Wallace in refuting use-inheritance.
The relative importance of natural selection as a cause of evolution is a scientific question. Its relative importance in defining the terms Darwinism and Neo-Darwinism to distinguish different doctrines is a conceptual issue.
Feel free to chime in with further relevant quotes from other times/authors.
---[update on Darwin's utilitarian doctrine, 16 April 2014]---
Carl Nägeli brings Darwin's utilitarian doctrine (Nützlichkeitstheorie) into his definition of Darwinism. It is therefore helpful to know what that utilitarian doctrine was. In The Origin of Species, Darwin (1859) dealt with Difficulties of Theory (chapter 6) in general and Organs of little apparent importance in particular. Some pages into that sub-chapter (p. 199-200) he wrote:
"The foregoing remarks lead me to say a few words on the protest lately made by some naturalists, against the utilitarian doctrine that every detail of structure has been produced for the good of its possessor. They believe that very many structures have been created for beauty in the eyes of man, or for mere variety. This doctrine, if true, would be absolutely fatal to my theory. Yet I fully admit that many structures are of no direct use to their possessors. Physical conditions probably have had some little effect on structure, quite independently of any good thus gained. Correlation of growth has no doubt played a most important part, and a useful modification of one part will often have entailed on other parts diversified changes of no direct use. So again characters which formerly were useful, or which formerly had arisen from correlation of growth, or from other unknown cause, may reappear from the law of reversion, though now of no direct use. The effects of sexual selection, when displayed in beauty to charm the females, can be called useful only in rather a forced sense. But by far the most important consideration is that the chief part of the organisation of every being is simply due to inheritance; and consequently, though each being assuredly is well fitted for its place in nature, many structures now have no direct relation to the habits of life of each species. [...] &c. Hence every detail of structure in every living creature (making some little allowance for the direct action of physical conditions) may be viewed, either as having been of special use to some ancestral form, or as being now of special use to the descendants of this form either directly, or indirectly through the complex laws of growth."
[My emphasis, here's an online version.]
This utilitarian doctrine is also implied in the first sentence of Weismann's quote below, where he said an organism consisted of adaptations new, old and ancient. Utilitarianism has later been exaggerated and criticized as adaptationism.
---[update on the term Neo-Darwinism, 22 April 2014]---
The term Neo-Darwinism is older than commonly believed today. In particular, it has a history before the modern evolutionary synthesis that is often called neo-Darwinian. Although most sources credit George Romanes (1883 or 1889) with coining the term Neo-Darwinism to designate the forms of Darwinism proposed by Alfred Wallace and August Weismann, I could not verify this attribution. The term appears in neither of these publications, but in his later book Darwin, and After Darwin (Romanes 1897). It's probably a mis-attribution.
The earliest source I could discover is by Samuel Butler (1880)—HT to George Beccaloni. Butler's usage of the term Neo-Darwinism may appear confused, because he applies it to Wallace and Charles Darwin somewhat indiscriminately, whereas it has later been used to distinguish the doctrines of Wallace and Weismann from Charles Darwin's. (Butler also applies the term Darwinism to Erasmus Darwin and Spencer, which a Whig retrospective would rather call Lamarckian.) Other terms to mark the difference between Charles Darwin on the one hand and Wallace or Weismann on the other have been pure Darwinism and ultra-Darwinism.
---[here come the quotes]---
"But the planetary orbits turned out to be not quite circular after all, and, grand as was the service of Copernicus rendered to science, Kepler and Newton had to come after him. What if the orbit of Darwinism should be a little too circular? What if species should offer residual phenomena, here and there, not explicable by natural selection?"
Huxley, T.H. 1860. Westminster Review 17 (n.s.) 541-570; reprinted in Collected Essays 2: 22-79.
"Die Nützlichkeitstheorie ist der Darwinismus. Man bezeichnet irrtümlicher Weise nicht selten als Darwinismus die Theorie, dass die Arten aus einander entstanden seien, und dass dies auf dem langsamen Wege der Racenbildung geschehen. Beides wurde lange vor Darwin ausgesprochen. Der grosse Fortschritt, den die Wissenschaft diesem Forscher verdankt, beruht in der Idee, dass die Racen- und Artenbildung das Produkt der natürlichen Züchtung sei, welche durch den Kampf um das Dasein geleitet wird. Etwas anderes unter Darwinismus begreifen, heisst die Bedeutung Darwins verkennen und seinen Ruhm schmälern. Freilich wurde dieses sein Princip von manchem seiner Gegner nur halb oder auch gar nicht verstanden und daher auch oft schief und unrichtig beurtheilt."
Nägeli, C. 1865. Entstehung und Begriff der Naturhistorischen Art. Verlag der königlichen Akademie, München, p. 16, footnote.
The utilitarian theory is Darwinism. They often say that Darwinism was the theory that species arose from each other and that this happened through the slow development of races. Both has been said long before Darwin. The great progress that we owe to this researcher lies in the idea, that the development of races and species was the product of natural selection, which is conducted through through the struggle for existence. To understand something else as Darwinism means to misjudge Darwin's importance and to belittle his fame. Certainly, some of his opponents comprehended this, his, principle only by half or not at all and therefore also judged it askance or wrong."
My translation. [It is interesting to note that Nägeli saw the utilitarian doctrine as an alternative to progressionism, the idea that evolution follows a path upwards toward perfection.]
"Diese Selektions-Theorie is es, welche man mit vollem Rechte, ihrem alleinigen Urheber zu Ehren, als Darwinismus bezeichnen kann, während es nicht richtig ist, mit diesem Namen, wie es neuerdings häufig geschieht, die gesamte Deszendenz-Theorie zu belegen, die bereits von Lamarck als eine wissenschaftlich formulierte Theorie in die Biologie eingeführt worden ist, und die man daher entsprechend als Lamarckismus bezeichnen könnte.(Fußnote 1)
(Fußnote 1:) Die entgegengesetzte dogmatische Theorie von der absoluten Constanz und der selbstständigen Erschaffung der Species, kann eben so nach Cuvier, ihrem hervorragendsten Vertheidiger, Cuvierismus genannt werden."
Haeckel, E. 1866. Generelle Morphologie der Organismen. Zweiter Band: Allgemeine Entwicklungsgeschichte der Organismen. Georg Reimer, Berlin, p. 166.
"It is this theory of selection, which has rightly been called Darwinism, in honor of its sole author, while it is not correct to name the whole theory of descent thus, as is often done lately, because Lamarck has already introduced it as a scientific theory to biology, and it could therefore be called Lamarckism accordingly.(footnote 1)
(Footnote 1:) The contrary dogmatic theory of the absolute constancy and the independent creation of the species, can equally after Cuvier, its primary defendant, be called Cuvierism."
"From what has been said, it appears that Darwinism includes three distinct elements. First, evolution; or the assumption that all organic forms, vegetable and animal, have been evolved or developed from one, or a few, primordial living germs; second, that this evolution has been effected by natural selection, or the survival of the fittest; and third, and by far the most important and only distinctive element of his theory, that this natural selection is without design, being conducted by unintelligent physical causes. Neither the first nor the second of these elements constitute Darwinism; nor do the two combined."
Hodge, C. 1874. What is Darwinism? Scribner, Armstrong, and Company, New York, p. 49.
"I had not as yet seen that the principle I was contending for was Darwinian, not Neo-Darwinian. My pages still teemed with allusions to "natural selection," and I sometimes allowed myself to hope that "Life and Habit" was going to be an adjunct to Darwinism which no one would welcome more gladly than Mr. Darwin himself." (p. 33)
"I had as yet no idea that a writer [meaning Mivart 1871] could attack Neo-Darwinism without attacking evolution." (p. 34f)
Butler, S. 1880. Unconscious Memory. David Bogue, London. [Note that St. George Mivart (1871. Genesis of Species. Appleton and Co., New York) did not use the term Neo-Darwinism, though some of what he described may well have counted as Neo-Darwinism to others. On later pages (52, 280ff, 282ff), Butler confusingly attributes the term Neo-Darwinism (sometimes also spelled with lower case neo-) to Charles Darwin at times, to Wallace and you name 'em at others as well as the term Darwinism to Erasmus Darwin, Spencer and you name 'em. Nevertheless I included the above quote as the earliest use of the term Neo-Darwinism I could find.]
"Even in rejecting that phase of sexual selection depending on female choice, I insist on the greater efficacy of natural selection. This is pre-eminently the Darwinian doctrine, and I therefore claim for my book the position of being the advocate of pure Darwinism."
Wallace, A.R. 1889. Darwinism. MacMillan and Co. New York, p. viii.
"It was the opinion of Mr. Darwin that natural selection has been the chief, but not the only, cause of organic evolution; while, in the opinion of Mr. Wallace, natural selection has been the all and in all of such evolution—virtually the sole and only principle which has been concerned in the development both of life and of mind from the amoeba to the ape—although he further and curiously differs from Darwin in an opposite direction, by holding that natural selection can have had absolutely no part at all in the development of faculties distinctly human. Disregarding the latter and subordinate point of difference (a re-presentation of which in the concluding chapters of his present work I may however remark appears to me sadly like the feet of clay in a figure of iron, marring by its manifest weakness what would otherwise have been a complete and self-consistent monument of strength), let us first clearly understand to what it is that the major point of difference amounts." (p. 245f)
[...] "Now, it is evident that, according to this theory, natural selection; is constituted the one and only cause of organic evolution; and for this reason the followers of Weismann are in the habit of calling his doctrine "pure Darwinism," inasmuch as without invoking any aid from the Lamarckian principle above described, it constitutes the Darwinian principle of natural selection the sole, and not merely as he said "mein, means of modification." (p. 248)
[...] "On the other hand, it is no less manifest that this doctrine, although not pure Darwinism, assuredly is, and always has been, pure Wallaceism." (p. 248)
Romanes, G.J. 1889. Mr. Wallace on Darwinism. Contemporary Review 56: 244-258. [This review is often cited as the place where Romanes coined the term Neo-Darwinism, and so is a Letter to the Editor by Romanes (1883. Nature 27: 362-364). The actual term Neo-Darwinism appears in neither, however, although the review of Wallace's book Darwinism aptly describes what Romanes distinguished as Wallaceism and what later became known as Neo-Darwinism before the synthesis (see Bailey 1884 and Romanes 1897 below). For a good candidate of coining the term neo-Darwinism see Butler (1880) above.]
"Denn der Organismus besteht, wie ich schon früher sagte, aus Anpassungen, neuen, älteren und uralten, und was an primären Variationen in der Physiognomie der Arten etwa mitspielt, it wenig und von untergeordneter Bedeutung. Ich halte deshalb die Entdeckung der Naturzüchtung für eine der fundamentalsten, die auf dem Gebiete des Lebens jemals gemacht worden ist, eine Entdeckung, die allein genügt, den Namen Charles Darwin und Alfred Wallace die Unsterblichkeit zu sichern, und wenn meine Gegner mich als „Ultra-Darwinisten“ hinstellen, der das Princip des grossen Forschers ins Einseitige übertreibt, so macht das vielleicht auf manche ängstliche Gemüther Eindruck, welche das „juste-milieu“ überall schon im voraus für das Richtige halten, allein mir scheint, dass man niemals schon a priori sagen kann, wie weit ein Erklärungsprincip reicht, es muss erst versucht werden, und diesen Versuch gemacht zu haben, das ist mein Verbrechen oder mein Verdienst."
Weismann, A. 1893. Die Allmacht der Naturzüchtung. Eine Erwiderung an Herbert Spencer. Gustav Fischer, Jena, p. 63.
"Then the organism consists, as I have said before, of adaptations, new, old and ancient, and whatever plays a role in the primary variation of the physiognomy of the species is few and of minor importance. I therefore regard the discovery of natural selection as one of the most fundamental ones that has ever been made in the field of the life science, a discovery that suffices on its own to secure immortality for the names of Charles Darwin and Alfred Wallace, and if my opponents refer to me as an "ultra-Darwinist", who exaggerates and biases the principle of the great researcher, that may impress some anxious minds that in advance take the "juste-milieu" everywhere as the right one, however methinks, that it is impossible to tell a priori, how far an explanatory principle reaches, it needs to be tested first, and to have undertaken this trial, that is my crime or credit."
"This, then, is Darwinism—that the controlling factor or process in evolution is selective: the survival, in the struggle for existence, of those individuals which are best fitted to survive." (p. 662f)
[...] "We are particularly concerned in its results, which are the distinguished marks of Neo-Darwinism—that the variation is of sexual or internal origin, and that acquired characters are not hereditary." (p. 668)
Bailey, L.H. 1894. Neo-Lamarckism and Neo-Darwinism. The American Naturalist 28: 661-678. [After defining the core of Darwinism on p. 662f, Bailey admits various correlative or incidental hypothesis attached to it. He continues to define Neo-Darwinism as Weismannism and in opposition to Neo-Lamarckism.]
"This question is whether natural selection has been the sole, or but the main, cause of organic evolution." (p. 1)
[...] "Now Darwin's answer to this question was distinct and unequivocal. he stoutly resisted the doctrine that natural selection was to be regarded as the only cause of organic evolution. On the other hand, this opinion was—and still continues to be—persistently maintained by Mr. Wallace." (p. 2)
[...] "Yet so greatly have some of the Neo-Darwinians misunderstood the teachings of Darwin, that they represent as "Darwian heresy" any suggestions in the way of factors "supplementary to," or "Co-operative with" natural selection." (p. 11)
[...] "Weismann's Essays on Heredity (which argue that natural selection is the only possible cause of adaptive modification) and Wallace's work on Darwinism (which in all the respects where any charge of "heresy" is concerned directly contradict the doctrines of Darwin)—these are the writings which are now habitually represented by the Neo-Darwinians as setting forth the views of Darwin in their "pure" form." (p. 12)
Romanes, G.J. 1897. Darwin, and After Darwin, vol. II. The Open Court Publishing Company, Chicago.
"Consequently, when my attention was drawn, later on, to the relations between Darwinism and Sociology, I could agree with none of the works and pamphlets that had been written upon this important subject. They all endeavoured to prove that Man, owing to his higher intelligence and knowledge, may mitigate the harshness of the struggle for life between men; but they all recognized at the same time that the struggle for the means of existence, of every animal against all its congeners, and of every man against all other men, was "a law of Nature." This view, however, I could not accept, because I was persuaded that to admit a pitiless inner war for life within each species, and to see in that war a condition of progress, was to admit something which not only had not yet been proved, but also lacked confirmation from direct observation."
Kropotkin, P. 1902. Mutual Aid. McClure, New York.
"—the fact is that the name Darwinism has been pretty consistently applied by biologists only to those theories practically original with Darwin which offer a mechanical explanation of the accepted fact of descent. Of these Darwinian theories the primary and all-important one is that of natural selection."
Kellogg, V.L. 1907. Darwinism To-day. Henry Holt, New York.
"In the mind of the general public Darwinism stands to-day for evolution. The establishment of the theory of evolution is generally accepted as Darwin's chief contribution to human thought, and while Darwin did not originate this idea that forms the framework of our modern thinking, yet by general accord its acceptance is attributable, and justly so, to Darwin.
To the zoologist Darwinism means more especially evolution accounted for by the theory of natural selection, yet also many other things, to which I shall refer in the proper place." (p. 367)
[...] "There is a small group of writers scattered amongst these larger groups that are ranked or rank themselves Neo-Darwinians. I must pause a moment to pay them my tardy respects. They have set themselves up to be the true Darwinians. They seem less concerned with the advancement of the study of evolution than with expounding Darwinism as dogma. Their credulity is more remarkable than their judgment. To imagine a use for an organ is for them equivalent to explaining its origin by natural selection without further inquiry. Any examination, in fact, into the nature of variation, they appear to regard as superfluous, although harmless, but it is heresy to study critically the working out of the theory of natural selection. Such has ever been the procedure of the infertile followers of great leaders. In the present instance the result is the more deplorable, since Darwin's own independence of the traditions of all schools, his careful study of facts, his emancipation from prejudice, are his lasting virtues. The Neo-Darwinian, worshipping the letter of the law, forgets its import. Let us salute, and pass." (p. 373f)
[...] "We stand to-day on the foundations laid fifty years ago. Darwin's method is our method, the way he pointed out we follow, not as the advocates of a dogma, not as the disciples of any particular creed, but the avowed adherents of a method of investigation whose inauguration we owe chiefly to Charles Darwin. For it is this spirit of Darwinism, not its formula, that we proclaim as our best heritage." (p. 380)
Morgan, T.H. 1909. For Darwin. Popular Science Monthly 74: 367-380.
"The controversies about evolution lie in the realm of the relative importance of various forces in molding evolution. One such controversy concerns the relative importance of direct "adaptive" natural selection for characters, as opposed to other forces of evolution such as genetic drift, genetic linkage, pleiotropy, allometry, and multiple adaptive peaks as explanations for particular events in evolution. A major cause of much of the present controversy—and the rich opportunity it affords creationists to find out-of-context quotations—is the growth of a vulgar Darwinism that sees direct adaptation in every feature of life. By making claims for natural selection that are as tortured as the absurd claims of the 19th century evolutionists who saw God's wisdom in everything, the vulgar adaptationists seriously weaken the power of evolutionary explanation. When called to account, they declare those who dispute them to be anti-Darwinians and even anti-evolutionists. And all the while creationists smile and take notes."
Lewontin, R.C. 1981. Evolution/creation debate: a time for truth. BioScience 31: 559.
"The second basis of modern biology is the assumption that the Darwinian process of natural selection accounts for all aspects of the adaptation of an organism to a particular way of life in a particular environment."
Williams, G.C. 1992. Natural Selection. Domains, Levels and Challenges. Oxford University Press, p. 5.
For German readers the following article may also be useful:
Junker, T. 2009. Was ist Darwinismus? Aufklärung und Kritik, special issue 15: 21-28.
And for English readers the following web-site by George Beccaloni is useful:
On the terms "Darwinism" and "Neo-Darwinism."