The Postman's Game
In Majora's Mask, the Postman will ask you to play a minigame in which you have to stop the clock after 10 seconds. This can be fairly difficult because the time disappears when the game starts. However, if you equip the Bunny Hood before starting the game, the timer stays onscreen and you can win every time. This is a great way to make money quickly because he pays 50 rupees a game after you win twice.
New Ending
To access this cheat, you have to beat Majora at least once. When you beat the game a second time, the cutscene you see before entering the moon will be different.
Play as Epona
Ride Epona to Milk Road. You'll find an Owl Statue in this area. Assign the Zora Mask to one of the "C" buttons, save and reload the game. When the game restarts, you should be back in the same place. Equip the Zora Mask and you'll transform, becoming too large to fit on Epona. Now you can control Epona and have her run all over the place without Link. To reverse this, just reset the game. This also works at the Owl Statue in Southern Swamp.
Disappearing Sword
This cheat works with the Great Fairy's Sword, which you receive by finding all 15 stray fairies in the Stone Tower Temple. Once you have the sword, go to Clock Town. Attempt to put the sword in the mailbox here. You'll get a message saying you can't do it, but the sword disappears. Link still poses his hands as if he's holding it, and if you attack something, the sword still works.
New Opening
When the game loads after powering on the system, press "Start" to go to the Main Menu. Highlight and select Options by pressing "Up" and "A." When the Options screen appears, quickly press "B" twice to go back to the intro screen. If done correctly, the opening sequence will be different.