Definition of or research on fun
Oddly enough, the place where you find the most information about this topic is where there's a lot of money to be made from it.   Facebook games or games in general.   If you focus on "why do people like to play some games and not others", then you're asking more of an economical question, and there will be a lot more information on the topic.

Example:
Funology: From Usability to Enjoyment (Human-Computer Interaction Series)

There's plenty of other works of this kind.

If you want things that are not related to games, I recommend Bruce C. Daniels's Puritans At Play: Leisure and Recreation in Early New England.

I believe both of these are available on Open Library.