Use of games in mentoring programs

This topic started as a series of emails over on our Department of Education grantee listserv, but I thought I'd move it over here for some wider discussion. The question is: what role do games (things like chess, board games, educational games, computer games, etc.) play in mentoring relationships, and how are programs integrating games with other mentoring activities?

There is a lot of good research (from folks like John Harris and Mike Nakkula) on the important role of fun and sharing in mentoring relationships, so it seems "game time" has a real basis in the theoretical models of how mentoring works best.

So tell us, how are games being used in your program? Recommendations of specific games that seem to be a hit are also encouraged.