Uh, sorry Adam, I will have to decline your challenge.
My personal favorite, though technically not a monkey, is Every Which Way But Loose, starring Clint Eastwood and Clyde the Orangutang.
I don't think this came out to a trilogy, because Clyde attacked Clint a couple of times while they were filming. Of course, maybe Clint was upset at being upstaged by an orangutang.
Again, not technically a monkey, and not technically a movie...but BJ & The Bear to me was the top of the heap when it came to Man and his primate buddy.