What do the White Walkers do with the baby boy gifts from Craster?
In the television series, we have yet to see what exactly the white walkers do with Craster's sons. Craster, for his part, tells Mormont that he "sacrifices" his children to the "real gods", implying that Craster (at least) assumes they are dead. However, we never see what became of the one son that Jon Snow saw being carried off.
In the novels, we don't actually "see" this event, but we do hear about it from Craster's wives. They claim to Jon and Sam that the sacrificed babies become Others (the book's term for the show's "white walkers"), and that this is how that species "procreates". However, we have not actually seen any Other that was positively identified as one of Craster's sons, so that is likely supposition on the part of the wives.
My suspicion is that the novel's claim is correct, and that we will eventually see this come up again in future seasons.
Edit: on television, in Series 4, in the episode "Oathkeeper" we actually see Craster's last son becoming a White Walker.
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@einpoklum because they didn't die, so they are not wights. His eyes turned blue (just like the other white walkers), we can however not be sure he is turned into a white walker but it's a solid theory check this link for more info http://gameofthrones.wikia.com/wiki/Craster%27s_last_son
`that he "sacrifices" his children to the "real gods", implying that Craster (at least) assumes they are dead` Sacrifice doesn't necessarily imply death. Giving something up is also a sacrifice. Craster has less use for boys than girls (due to his incestuous habits), but he could still use boys (for physical labor and/or protection), and having to give them up is therefore a sacrifice. Craster **could** think they're dead (because he doesn't know what happens to them), but it's also possible that he doesn't think they're dead. His words are ambiguous.
@JDoe yes, little Sam is Craster's last son (we know of) that is fully alive (as in not a white walker)
Regarding the edit at the end of the answer, we seem to see the last baby being turned into a *baby* white walker. And we are then left to wonder if there is some kind of growth acceleration that goes along with that or will it take 16 - 20 years before that baby is leading armies and raising dead like the rest of them.