Bugs

Infinite Fairy in a Bottle
When you collect your first bottle, find a fairy and catch her in the bottle. Then anytime you are in a room where you can walk off the screen get close to the exit and use your fairy while Link is looking at you (towards the screen). If done correctly (gets easier with practice) the screen will shift behind him and he'll exit while the fairy is being used, and on the next screen, you will have gained all your life back and the fairy still in reserve.

Hyrule Courtyard Friends
When your young Link and first sneak into the castle to talk to Zelda, before you go see her walk to the right (as soon as you walk into the courtyard facing Zelda) to the window. If you look through the window you'll notice pictures and paintings in some room with Mario, Bowser, Luigi, Yoshi, and the Princess! Stand to the right of the window and use the up C button to look at Yoshi, look at Luigi and if you shoot the window with your sling shot you'll get a Red Rupee.

Catch a Butterfly
Whenever you see butterflies, you can whip out your Deku stick and carefully place the end on the butterfly. If done correctly, the butterfly will turn into a fairy, and you can catch it with your bottle. It is quite hard to do, but it is possible. If you are having trouble, try swinging your Deku stick at the butterfly.

Lost Woods Path
When walking through the Lost Woods and are not sure if the path will send you back try this trick. If you walk up to a path that has brown in the middle it will send you back(unless it is the Sacred Forest Area). If it is just a black background, you can walk through it.