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2.
A drinking game where the object of the game is to bounce a ping pong ball off of the table, off your partners "titties", and into the cups in front of them.

Titty cup is played with 4 people (2 teams of partners) on a beer pong or similar sized table. Sets of partners stand diagonally across from one another. Each person has 3 cups in front of them in a triangle, and there needs to be one water cup ready to be put on the table. Each team has a ping pong ball. The goal of the game is to bounce your ball off of the table, then off of your partners titties/chest and into the cups in front of them. Once a cup is made, the opposing player next to the cup that was made must drink the cup, and then flip it on to the table flip cup style. During this drinking/flipping period, the team is not allowed to bounce, but the team that made the bounce continues to play. Once all of a teams cups are gone, they put the water cup in the middle of the table and take turns attempting to double bounce the ball into the cup. Once the double bounce is made, the game is over. During this time the other team continues play as original.

Any amount of alcohol can be in the cups, but half a beer per 3 cups in a good amount

A "slam dunk" occurs when a play "catches' the ball on/in their titties, and drops it into the cup
"Another slam dunk? She really has some titty cup 'talent'"

A titty cup tournament is best played with male female sets of partners
by gooseman October 08, 2012
 
1.
Another name for a bra.
Hey Jon, look at those titty cups she is wearing.
by S Richards. August 23, 2008