I think this is a trick question. It seems that if I want a game, I have to run the game. I've got a crowd of players who irregularly are willing to show up to games when I run them, but rounding them up can be like herding stray cats... and there's never the opportunity to just sit back and let someone else do the heavy lifting.
The only real time I get to relax with a game is when I go to a convention, and even then it's more a case of knowing who is on the table more than knowing what game we're playing.
I can honestly say that I don't have an answer to this one.