Save Cheat
The Legend of Zelda is notorious for not having a conventional save system. There is, however, a way to save your progress whenever you want. Doing so requires two controllers. When you want to save, pause the game with the first controller. Then, using the second controller, press Up and A at the same time. This opens the secret save menu, allowing you to save your progress and load previously saved games.
Restore Health
This cheat works at any Great Fairy lake. As you approach the lake and your health begins to regenerate, pause the game and activate the secret save menu. Save your progress and then load the data you just created. When the game restarts, you will be at full health.
The Second Quest
The game's second quest, which is essentially a more difficult version of the first quest, becomes available immediately after beating the game the first time, but there is a trick to unlocking it fully. Start the game as you normally would, but when it asks for you to put in a name, enter "Zelda." When the game begins, you will be playing the second quest.
Keyless Entry
This cheat only works on the Level 1 dungeon. Enter the dungeon and exit immediately. When you go back into the dungeon, you'll notice the door to the north has unlocked without the use of a key.
One-Second Gohma Battle
There is a secret way to defeat Gohma almost instantly. As you make your way to his boss arena, ready your bow and arrow. When you enter, he will be facing you with his eye open. Fire an arrow the second you enter the door and Gohma will die, making you the victor.