Song of Storms
A,CD,CU,A,CD,CU
Causes it to rain.  Allows you to enter the bottom of the well as young Link.  Also used to open secret holes and summon secret Big Fairies. Talk to the weird guy inside the windmill in Kakariko Village as adult Link and then show him your Ocarina (equip Ocarina and push the Ocarina button when near him).

Minuet of Forest
A,CU,CL,CR,CL,CR
Warps you to the Sacred Forest Meadow Learn from Sheik when you get to the Sacred Forest Meadow as adult Link.

Bolero of Fire
CD,A,CD,A,CR,CD,CR,CD
Warps you to the Death Mountain Crater Learn from Sheik on your way to the Temple of Fire

Serenade of Water
A,CD,CR,CR,CL
Warps you to the entrance to the Temple of Water in Lake Hylia Learn from Sheik when you get the Iron Boots in the Ice Cavern

Nocturne of Shadow
CL,CR,CR,A,CL,CR,CD
Warps you to back of Kakariko Graveyard, entrance to Shadow Temple. Learn from Sheik if you return to Kakariko Village after beating the Water Temple.

Requiem of Spirit
A,CD,A,CR,CD,A
Warps you to the entrance to the Spirit Temple, the Desert Colossus
Learn from Sheik after crossing the desert, going into the Spirit Temple, then coming back out again.

Prelude of Light
CU,CR,CU,CR,CL,CU
Warps you to the Temple of Time Learn from Sheik if you return to the Temple of Time's Master Sword room after beating the Forest Temple level.

Player-defined
Scarecrow's Song - summons a scarecrow at certain areas that you can use your hookshot on to get to things.  Look for areas where Navi turns green but there doesn't seem to be anything there. To get this song, go as young Link to Lake Hylia and look for a small farm area with a scarecrow in it in the Northern section.  Show him your Ocarina and he'll ask you to compose a tune.  The tune has to be 8 notes long.  Make it easy to remember.  Now as adult Link return to the scarecrow and play the same song for him again.  Now the song you made up becomes the secret Scarecrow's song.