I know that human poachers hunt gorillas and chimps on occasion. What other animals kill them with any degree of regularity?
Going off of various tv documentaries: big cats, if the primates live in areas with big cats. Although, I think this might be more for the baby primates, who are easier to pick off.
I wonder if lions think human tastes like chimp? 
According to Safari Quest:
the primary predators of the chimpanzee are man, leopards, baboons and large snakes.
According to Kilamnajro.com
Outside of the occasional leopard, humans are the greatest predator of the Mountain Gorilla
As to the lowland gorillas [eastern and western] besides man, the African Wildlife Foundation says Leopards and crocodiles
Ive heard of chimps going cannibalistic on occasion. That count?