there are two really popular ones that we play where i'm from!
the first is called Beer Pong. you play on a long table, one team on each side. each side has 10 cups filled like 25% with usually beer/seltzer (set up similar to bowling pins 4-3-2-1 setup), and basically each side takes turns throwing ping pong balls, trying to make the ping pong balls land in the cups on the other side. each time a team lands a ping pong ball into a cup, the opposing team has to drink the alcohol in the cup. there are various rules you can play, but first side to get balls into all the cups win
the second is called Rage Cage. this one is a bit harder to explain, but there are a bunch of cups with beer/seltzer on a table and there is a "bitch" cup in the middle usually filled with a variety of alcohol. the first two people start by drinking a cup, and trying to bounce a ping pong ball off the table, into the cup they just drank. when you land the ball into the cup, you pass the cup+ball to the next person, but if you make it in on your first try, you can pass the cup to whoever you want. if the person in rotation gets their ping pong ball into their cup before you, they stack their cup on top of yours and you have to pass your stacked cup to the next person, drink from one of the filled cups in the middle, and then try to get your ping pong ball in the cup until there are no more cups on the table. there's a term in the game called "caging" someone, where you can basically trap a player by continuously stacking & forcing them to drink if other players can keep landing their shots in one try