Mitosis (for those who don't know what it is, google it. I'm not going to start explaining how it works...) is most likely going to be in cellular stage, but would it be possible that it stays for the species at aware stage and beyond? This would also allow genderless species I think. I don't know if it is exactly evolutionary possible, but it would be awesome to see it in game. And it wouldn't even be that hard to program. Maybr even easier than the usual breeding.
Hydras, jellyfish (in the polyp stage), flatworms, and a bunch of other structurally-simple organisms reproduce by budding. As for why, you'd have to google, as I don't have the time for more than quick responses atm.