You do realize that over half of all animal species live in tropical rain forests; it would be a long list of animals. It also depends which rain forest you are talking about (the Amazon, Congo?). However, a lot of rainforests do essentialy have a lot of the basic kinds of animals. Here are a couple:
Large spotted cat (leopard in old world and jaguar in new world)
Various monkeys as well as every species of ape
Serpent and Monkey eagles (Harpy Eagle is one of them)
Various boas and pythons as well as plenty of elapids and vipers
Parakeets and parrots
some type of army ants (driver ants)
small antelope or deer
forest pigs or pecceries
many different beetles and bugs
venomous frogs (poison arrow dart frogs anybody?)
Various civets, mongooses, and small felids
many unusual bird families
As I said, there are many animal species, but these are some of the typical animal kinds you will find in most rainforests (not everyone, though). Need any specific species?