Look around.  If you're stuck in a dungeon, its probably because you've failed to see something painfully obvious to the rest of us.

Listen to Navi.  If you're stuck because you don't know what to do next, she'll usually tell you.                                                               

Talk to everyone!  They give good hints.                                                               

Some things can be used in more than one way (a deku stick can be a torch, an arrow can be caught on fire, etc.).                                                              

Look at your maps.  They can tell you where you need to go.

Whenever anyone mentions music of any kind, take out your ocarina, and see what happens.

If it looks suspicious, bomb it.

If you can beat the running man as an adult after you fix the bridge over Gerudo Valley in less than 50 seconds, you can get the king's wallet, which holds 1000 rupees!

If you're a kid, walk on the chain on the drawbridge to Hyrule City, and wait 'till night.  You can ride it up to rupees.

At the desert Colossus, if you have grown the magic plant, it is possible to ride it to an elevation that will allow you to shoot the longshot at the chest containing the mirror shield get it without the hassle of going through the dungeon (I've not been able to do this, but I'm told it's possible.).

Play Zelda's Lullaby for the gossip stones, and they'll give you fairies.

If you place a bomb next to a gossip stone and let it explode, the gossip stone will flash, then take off like a rocket into the sky.  This really does nothing, but it's really kinda cool.

If you destroy a sign, then play Zelda's Lullaby in front of it, you can watch it regrow before your eyes.

If you return to the skull kid in the Lost Woods and kill him as an adult, you can get two hundred rupees per time!