Gold Rush
Collect lots of coins, essentially. I haven't played Gold Rush in ages, so I can't really give you a good description.

Ground Force
Most people know this as Survivor because they watch too many stupid reality TV shows. Shoot blocks and don't fall off the level.

Single Player
Make your way through a series of levels, shooting badguys along the way.

Bank Robbery
One team tries to steal coins from a base while the other defends. After a while, the two teams switch.

Trivia
A host will ask questions and the players must answer. Depending on the host, the rules may vary.

Tests
There are many different types of tests. In most of them, you have to try to avoid touching a certain type of tile, or else you have to start at the beginning of the current test level you were in. Again, tests can be very different, especially EvilMike's Platform Tests.

Assassination
Try to kill the "king" or "leader" of the other team to score a point for your team. The leader of a team is usually given lots of powerups, access to carrots, etc.

Team Race
I wasn't aware that these existed, although many times I've wanted to try to make one.