Expert mode: - Enter ZELDA as a password.

Quit game: - Press Start on controller one, then hold Up + A on controller two.

All Weapons - Enter smmkghuj as a password.
Credit to Jack for this cheat

Avoid force battles - To avoid forced battles (battles by stepping on a certain tile on the field) simply wait in front of it until monsters appear and when one steps on the tile, move onto the tile and you'll go into a battle scene from the monster, not the tile. Most monster battle scenes are much easier than the tile's. Extremely useful when going to the Great Palace.
Credit to neoquester for this cheat

Warp Hole - In some castles and action screens it is possible to jump higher than the stats at the top of the screen. If the spell Fairy is used when Link is above the stats and you try to move to a side, he will fall through a warp hole. In the action screens Link will simply reappear on the same action screen. While, in the castles, he will end up on top of or in another room, on top of the castle entrance, or in an elevator below the castles entrance and stuck. If he gets stuck below the castle, you will need to reset the game. Also, the spell Jump can help with this glitch.
Credit to mog255 for this cheat

No keys - If you come to a locked door and hove no key you can simply use the Fairy spell and fly right throuogh the keyhole. And sometimes if you have enough magic you can make it through the whole palace just using this trick.
Credit to neoro for this cheat

Special Save Screen - Make sure you have two controllers in. Now on controller 1 pause the game, on controller 2 press up and A at the same time. You will be taken to a menu where you can save or continue.
Credit to Pyro Vesten for this cheat

Earn quick experience for new character - To quickly earn more experience for a new character, first have a character who is far along in the game but hasn't done all the palaces yet. Have this character beat a palace and go to the place to insert the gem. When you insert the gem and the experience points start to total up, pause and do the Quick Save. Then, load your new character. All of the experience points which would've gone to the character you beat the palace with will now go to your new character.
Credit to terrisus for this cheat