I have sometimes heard it said that Alfred Russel Wallace coined the term "Darwinism". This is incorrect, although he did use the term (perhaps unfortunately!) as the title of an excellent book about evolution which he published in 1889. The term "Darwinism" (as relating to Charles Darwin's theories rather than to his grandfather Erasmus' ideas) was actually first used by "Darwin's Bulldog" Thomas Henry Huxley in a review he wrote of Darwin's "Origin of Species" in 1860. Curiously, the related term "neo-Darwinism", which refers to the 'modern' view of Darwinism minus the inheritance of acquired characters (i.e. Darwinism without Lamarckism), was coined by Samuel Butler in 1880 with reference to Alfred Russel Wallace's views on evolution. Wallace rejected Lamarckism throughout his long life, correctly insisting that natural selection is the primary mechanism of evolutionary change and that traits acquired by organisms during their lifetime (e.g. a blacksmith's well developed arm muscles) are not inherited by their offspring.
Wallace's first published rejection of Lamarckism was in his 'Ternate' essay of 1858 - which formed part of the famous paper in which he and Darwin proposed the theory of natural selection for the first time. Wallace wrote:
"The hypothesis of Lamarck — that progressive changes in species have been produced by the attempts of animals to increase the development of their own organs, and thus modify their structure and habits — has been repeatedly and easily refuted by all writers on the subject of varieties and species, and it seems to have been considered that when this was done the whole question has been finally settled; but the view here developed renders such an hypothesis quite unnecessary, by showing that similar results must be produced by the action of principles constantly at work in nature...Neither did the giraffe acquire its long neck by desiring to reach the foliage of the more lofty shrubs, and constantly stretching its neck for the purpose, but because any varieties which occurred among its antitypes [ancestors] with a longer neck than usual at once secured a fresh range of pasture over the same ground as their shorter-necked companions, and on the first scarcity of food were thereby enabled to outlive them."
Perhaps suprisingly, Darwin always believed that Lamarckism (what he called "use and disuse" inheritance) played a role in evolution alongside natural selection and in 1868 he even proposed a now descredited theory, called Pangenesis, to explain how it might work1. I find it ironic that not only was the term "neo-Darwinism" proposed with reference to Wallace's evolutionary views, but that Wallace was actually the first ever neo-Darwinian! He was even more "Darwinian" than Darwin himself and can be regarded as being the first 'modern' evolutionary biologist. "Neo-Darwinism" should really be replaced by the term "Wallaceism" instead!
The term "neo-Darwinism" is usually said to have been coined by George Romanes in 1888 (often erroneously stated to be 1895 or 1896), but it in fact dates back to Samuel Butler's book "Unconscious Memory" published in 1880. Butler use it in the sense described above and cited the above passage from Wallace's 1858 essay as an example of this view (which incidentally Butler disagreed with)!
The term "Wallaceism" was apparently coined by George Romanes in 1889 to refer to Wallace's view that evolutionary change is driven by natural selection alone and does not involve Lamarckism like Darwin believed. Romanes believed that Wallace was wrong, but it turns out that Romanes was!
1. In his 1905 autobiography My Life, Wallace remarks: "Pangenesis, and the Heredity of Acquired Characters.—Darwin always believed in the inheritance of acquired characters, such as the effects of use and disuse of organs and of climate, food, etc., on the individual, as did almost every naturalist, and his theory of pangenesis was invented to explain this among other affects of heredity. I therefore accepted pangenesis at first, because I have always felt it a relief (as did Darwin) to have some hypothesis, however provisional and improbable, that would serve to explain the facts; and I told him that "I shall never be able to give it up till a better one supplies its place." I never imagined that it could be directly disproved, but Mr. F. Galton's experiments of transfusing a large quantity of the blood of rabbits into other individuals of quite different breeds, and afterwards finding that the progeny was not in the slightest degree altered, did seem to me to be very nearly a disproof, although Darwin did not accept it as such. But when, at a much later period, Dr. Weismann showed that there is actually no valid evidence for the transmission of such characters, and when he further set forth a mass of evidence in support of his theory of the continuity of the germ-plasm, the "better theory" was found, and I finally gave up pangenesis as untenable. But this new theory really simplifies and strengthens the fundamental doctrine of natural selection.
It will thus appear that none of my differences of opinion from Darwin imply any real divergence as to the overwhelming importance of the great principle of natural selection, while in several directions I believe that I have extended and strengthened it. The principle of "utility," which is one of its chief foundation-stones, I have always advocated unreservedly; while in extending this principle to almost every kind and degree of coloration, and in maintaining the power of natural selection to increase the infertility of hybrid unions, I have considerably extended its range. Hence it is that some of my critics declare that I am more Darwinian than Darwin himself, and in this, I admit, they are not far wrong."
[Huxley, T.H.] 1860. Darwin On the origin of Species. Westminster Review, 17(n.s.): 541-70.
Romanes, G. 1889. Mr. Wallace on Darwinism. Contemporary Review, 56: 244-258.