There is some research with great apes that makes the rounds every now and then but the findings are dubious at best as there's a lot of conflict of interest, handwaving and wishful thinking (see Koko "mourning" when told that Robin Williams died because they met once at some point in the past).
EDIT: Also it's probably a good idea to limit the conversation to social animals. Solitary animals don't have much use for communication other than challenging the competition and impressing potential mates -- insert celebrity joke here.