"Run Red Run" by the Coasters. Unbelievable song! "Well, Red went and bought himself a monkey... bought it from a pawn shop broker. Taught that monkey how to guzzle beer, and he taught him how to play stud poker. Well last night they was gamblin in the kitchen, and the monkey he was taking a beatin'; the monkey said "Red, I'm gonna shoot you dead, cause I know dang well you been a cheatin'!""
Or "Harry the Hairy Ape" by Ray Stevens. Another golden oldie.
"Super Ape" by the Upsetters (Lee Perry). Legendary song/LP - probably the best Dub Reggae LP of all time.
"Gorilla Girl" by the Dead Milkmen... lame goofy punk/indy rock, but you did say any/all.
"Planet of the Apes" by the Dehumanizers. Punk/metal.
And can't forget "Lancelot Link and the Evolution Revolution", a bubble-gum pop LP that went along with the famous live-acting chimp spy comic from the 60s.
ok, I'll stop. "Run Red Run" is worth looking into, it's a hoot, and great classic soul/r&b by a real feel-good band.