All of the great apes – orangutans, gorillas, chimpanzees and bonobos – respond to being tickled with a remarkably human-like laugh.
Ticklishness may have even more ancient evolutionary roots than that. Rats, for example, giggle ultrasonically when tickled by humans. Dogs, meerkats, penguins and many others also seem to enjoy it.
Ticklishness is a strange mixture of pleasure and pain – indeed, pain receptors in the skin are heavily involved in the sensation.
Just like humans, rats need to be in the right mood for it, though. In a relaxed setting, they will solicit the attentions of a tickler, but avoid it when they are anxious.
The function – if there is one – is far from clear. One possibility is that it is a form of play-fighting between mutually trusting individuals.