I'm disappointed in you all. Link's Awakening doesn't have a secret ending. It just shows a picture of Marin if you beat the game without dying.
These are the only Zelda games with MULTIPLE endings:
Completely different endings:
Ancient Stone Tablets - If you fail to complete all the dungeons in time, you'll get a bad ending.
Oracle of Ages/Seasons - Both games had the regular ending, and a second "true" ending when you use the password from the other game.
A Link to the Past (GBA version) - if you beat the secret dungeon, you'll get another ending.
Slight variation endings:
Legend of Zelda - You'll get a different congratulatory message if you beat the second quest.
Link's Awakening - Shows a picture of Marin after the credits if you beat the game without dying.
Majora's Mask - During the credits, scenes will not happen if you didn't find the masks relating to those characters. The masks missing will be shown instead.
Spirit Tracks - Before the last battle, Zelda will ask what you want to be. Depending on what you answer, you'll see three different scenes after the credits.