Spoiler (Highlight to read):
There's obviously the fishing mini-game; in which of course you obviously fish.
There's the STAR mini-game. Which you're put in a cage and are supposed to collect these balls of light using the in-game item called the "clawshot" and the "double clawshot" within the time limit.
There's the Fruit Pop Flight Challenge mini-game; in which you're supposed to fly with a giant flying bird-like creature as Wolf Link while avoiding the walls and different obstacles and trying to pop as many balloons as you can.
Then there's the Flight-By-Fowl mini-game (which is hardly a mini-game at all). You simply grab a cucco and jump off a high area. The main point of the game is to slowly descend to some platforms below (with the option of collecting rupees on the way down).
There's also a snowboarding mini-game. The object of the game is to race down the mountain to beat the other "person." You have avoid certain obstacles and jump at certain areas in order to defeat the other "snowboarder".
There's a mini-game called Roll-Goal in which you're supposed to guide a little ball along narrow paths until you help it reach its destination.
Then finally there's the Rapid Ride mini-game. In this mini-game, you raft down a river using a canoe while trying to hit targets with your bomb and arrow combination. You also have to make you sure you don't bump into any walls or else you lose a point.
There is no shooting gallery in TP sadly. TP was lacking in the mini-game department.
I'm pretty sure that's all the mini-games in TP.