Are they throwing them? In college when we played, it was 2 on 2, with ping pong paddles. In front of each person was a large SOLO cup of beer. If you hit another person's cup, they drank a sip. If you landed the ball in the cup, they drank the whole cup. If you knocked your own cup over with your paddle, you filled it up and drank the whole cup.
Now, in high school, we used to play a game we called Beirut. 4 people, each team had 8 or so Solo cups in front of them. There were at least 4 ping pong balls. You threw them at the other teams cups, and when you got one in someone from the other team had to drink the whole cup. Needless to say, people got ripped pretty fast. We used to have a large garbage can next to the table so that people could puke and rally.
This is Beirut...but they're using the wrong name. I also played Beer Pong with Ping-Pong Paddles and two cups per side. I've played variations of Beirut with 6 or 10 cups.