I'll have to admit, my bunch isn't much for traditional board games. Some board games are designed so that they encourage interaction between the players, and the action of playing them is the fun bit, and the "game" part of it is largely an excuse - such games would work well.
So: Encore, Apples to Apples, Once Upon a Time, are all good games for my group. Risk and Settlers of Catan, not so much.
For pick-up roleplaying, I suspect the Superhero genre in general is a god bet - the basic unit of story is like an issue of a comic book, and you dont' need to prep up much for that. And most supers systems are simple enough in rules that players can have fun without having to dig too deeply into them.
Paranoia, of course, is a classic one-shot pickup game.