Henry Gee comments in the Guardian about the other kind of hobbits, featuring orc reproductive biology: "Hobbits and hypotheses".
In the Silmarillion Tolkien says in one throwaway line that orcs reproduced the old-fashioned way. Boy orcs and girl orcs would get together to produce baby orcs. But this doesn't square with the evidence. Never do we see any explicitly female orcs. Sure, Middle-earth is a bit like a boys' own fantasy, so this might not be a surprise. However, Tolkien goes to great pains to mention the existence of females in every other species, even when as in the dwarves and the ents they are offstage.
Elsewhere, Tolkien says that Morgoth (Sauron's boss) created orcs from captured and tortured elves, but that could hardly supply enough orcs to make a small platoon, let alone armies. There had to be a way of creating orcs from other orcs.
In The Science of Middle-earth I offer a suggestion that is at the same time radical and yet consistent with the evidence orcs are, in some circumstances, parthenogenetic.
I think an anthropological explanation is more likely. Tolkien's sympathetic races concern themselves with "home and family" themes, the unsympathetic races don't. We don't really get much of a look into orc culture, or the culture of the Men of Harad, for that matter, and this blind spot is intentional; without which it would be more difficult for the reader to accept them as morally inferior races.