GURPS has some good rules for drinking. But they really need punching up for a good drinking contest.
These rules are probably less realistic than they could be, but if you want to slam down drinks in a Dungeon Fantasy tavern they'll do well.
Who can pound back the most drinks and stay standing? Winner is the last person still conscious. No extra points if your opponent slips into a coma.
Drinks: One drink is 12 oz of beer, 4-5 oz of wine, or 1.5 oz of spirits - although special drinks may count as more or fewer drinks per serving.
Drinking Limit: You can drink up to HP/4 drinks before needing to make a roll against the higher of HT or Carousing. Modifiers and rules are per p. B440.
Optional rule: Use Trained HP. Carousing @ HT+1 gives a +1 per 10 HP, @ HT+2 gives a +2 per 10 HP, etc. using the Fast progression from Martial Arts: Technical Grappling. For simplicity you can stop the progressing at +2 @ Stat+2. Use that final score to determine HP before dividing by 4 to handle your drinks. A large, experienced drinker can hold a bit more in these contests!
It should probably go without saying that all other contests are better - more fun for the players and the GM, that is - if the characters involved drink first. Let the last delvers standing commence with the next contests!
Who can eat the most?
Meals: Rate all food in meal-sized servings - roughly 8 oz of dry food (more if fresh - assume 16 oz. fresh).
Eating Limit: You can eat up to HP/5 meals before needing to make a roll to force food down . . . or keep it down. Roll against the higher of HT or HT-based Cooking. Every meal after your limit is a -2 to the roll. Failure means you can't physically force it down and become Nauseous. Failure by 5+ means you a Vomiting; Critical Failure costs 1d FP and causes Vomiting.
Optional rule: Use Trained HP; Cooking (optionally, Survival) @ HT+1 gives a +1 per 10 HP, @ HT+2 gives a +2 per 10 HP, etc. using the Fast progression. For simplicity you can stop the progressing at +2 @ Stat+2.
Neither of these address the really horrible stuff, like drinking gross things or forcing down inedible, unappealing, or uncooperative food. I'll get to those tomorrow!