Paul F. Norris summarizes some recent research:
[C]himps laugh in response to the laughter of their playmates, that this laughter differs in acoustic form and timing from their spontaneous laughter, and that the purpose of their non-spontaneous laughter appears to be to prolong social play, promoting group cohesion and perhaps providing the chimps with important social advantages.
He looks at the science on rat laughing here.
The Dish 