What you can do:
Arm Wrestling, Basket, Snowboarding, Submarine Game, 3D Fighter, Mog House, Motorcycle game, change your GP to prizes or money.

Arm Wrestling:
You wrestles against some opponents by pressing Circel. You can win GP

Basket :
Throw the ball into the basket by holding Circel. You can win GP

Snowboarding:
Slide down a mountain on board, win stuffs and beat your own record. Pick ballons to reccive points.
When you have managed to conquer all three hills, you will be able to race against your own shadow, that will go down the mountain the same way as you did on your best race. Just for fun.

Submarine Game
Bomb other submarines in  the sea. You can win GP

3D Fighter
Fight against another fighter, by pressing square, triangel and circel and cross. You will win 3 gp after defeating the second one. Dont know how many fighters you can fight against. Think they are only three.
 
Mog House
Give Mog nuts so he can fly. Feed him untill he does another sound than usual, and he will be able to fly. DOnt know what you can win.

Motorcycle Game
A game verision of the motorcycle chase in the beginning of the game. Just for fun.

Changing GP to prizes or Gil
You can change GP to secret prizes and to Gil.
 

Special Items:
Cait Sith