“As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected.”

Source: On the Origin of Species (1859), chapter III: "Struggle For Existence", page 61 http://darwin-online.org.uk/content/frameset?pageseq=76&itemID=F373&viewtype=image
Context: Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring. The offspring, also, will thus have a better chance of surviving, for, of the many individuals of any species which are periodically born, but a small number can survive. I have called this principle, by which each slight variation, if useful, is preserved, by the term of Natural Selection, in order to mark its relation to man's power of selection.

5 January 1857 (p. 326)
1831 - 1863, Delacroix' 'Journal' (1847 – 1863)

This passage has been cited as an anticipation of the idea of punctuated equilibrium.
Source: On the Origin of Species (1859), chapter IV: "Natural Selection", page 105 http://darwin-online.org.uk/content/frameset?pageseq=120&itemID=F373&viewtype=image

Source: Ender's Game

Source: Beyond This Horizon (1948; originally serialized in 1942), Chapter 13, “No more privacy than a guppy in an aquarium”, p. 126

Message to the Tricontinental (1967)
Context: Each spilt drop of blood, in any country under whose flag one has not been born, is an experience passed on to those who survive, to be added later to the liberation struggle of his own country. And each nation liberated is a phase won in the battle for the liberation of one's own country.

1980s and later, Knowledge, Evolution and Society (1983), "Coping with Ignorance", "Our Moral Heritage"

Source: The Causes of Evolution (1932), Ch. IV Natural Selection, pp. 104-106.
Context: Where natural selection slackens, new forms may arise which would not survive under more rigid competition, and many ultimately hardy combinations will thus have a chance of arising.... Thus the distinction between the principal mammalian orders seems to have arisen during an orgy of variation in the early Eocene which followed the doom of the great reptiles... Since that date mammalian evolution has been a slower affair, largely a progressive improvement of the types originally laid down in the Eocene.
Another possible mode of making rapid evolutionary jumps is by hybridisation.... hybridisation (where the hybrids are fertile) usually causes an epidemic of variation in the second generation which may include new and valuable types which could not have arisen within a species by slower evolution.