Guitar Hero was the most annoying game when drunk, I had to drop down to Medium from Expert after a few songs because I was barely scraping through them.
Any GTA game when drunk with some mates is great, you just go on killing sprees doing stupid shit you wouldn't usually do, like going round little Haiti with a flamethrower shouting at 3 in the morning that you needed to cleanse Vice City.
Edit: As for a drinking game, the nastiest I've ever played involved a dirty pint (In this case it had beer, cider, spirits, vinegar and tomato ketchup), place a piece of tissue paper over the top of the glass, wetting the edges so they stay stuck to the edge of the glass, then place a penny or some other small coin the center. In turn everyone has to burn a hole in the tissue paper with either a cigarette or a joint. Whoever makes the penny drop, has to down the drink and spit the penny back into the glass.