...or 'Ape Oriented Platformer'.
Though the term is recent, this genre probably originated with the first Donkey Kong. However, there are still debates among fans of the genre over whether or not the original DK is a true AOP as the protagonist was Mario, not DK. Thus, some consider DK Jr to be more legit as it was much more ape-centric.
I disagree and contend that the story has to simply focus on primates specifically to merit the label. Monkey Ball comes close but is not quite a platformer, it merits the term A.O.P only in the fact that it is an "Ape Oriented Puzzler".
Anyways, my favorite in this genre has to be Ape Escape, the original for PS1, which seems to be largely overlooked in the west. I might actually prefer DK64 over the DKC series overall since, although the DKC series was great, I always felt it was rather overrated.
Toki could count as well but it wasn't exactly my cup of tea. Can't think of any others except Monkey Majik which I didn't hear a whole lot of good things about.