The one that immediately comes to mind is in Jak X: Combat Racing where you'd lose all of your money you've earned when you start a race. That's really the only game breaking glitch I can think of that has actually affected me.
Really awesome thing you're doing here. I would sign up, but I doubt I'll be playing many games on my 360 so I'll just leave my spot blank for someone more likely to win to have it. Good luck to everyone that enters!