The last Vampire game I ran everyone had to be tied in some way to the local mafia.
In the past, I've been even more narrow and run games where everyone had to be the same clan. (This actually went really well, and the next time I do VtR, I will probably do it again, although maybe same Covenant.)
For my current game, Orpheus, I basically just explained to everyone that the characters would be investigators, that it would be their job to go in and solve mysteries and the like. Characters should be smart enough to do this, and not so insane or loose cannons that they can't function in a work environment.
Evernight didn't have any restrictions, partly because it was a very classic D&Desque fantasy world, so everyone knew the basic ideas right away, and partly because the idea of the campaign was that you are the huddled together resistance fighting against the unstoppable alien overlords, so most anyone who could swing a sword or be otherwise useful was a fine PC.
But anyways, when you do put restrictions or guidelines down for a game, what sorts of things do you do or have you done?