It looks to me like there were three of them. I'm going to just copy-paste from wikipedia about them.
Link: The Faces of Evil
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The lands of Hyrule are at last peaceful, so what more can a hero do? Link, feeling increasingly useless in this safe environment, has no idea that the far away island of Koridai has been taken over by his old nemesis, Ganon. Worse, he has kidnapped the Princess of Hyrule, Zelda, and is holding her captive there. A mysterious wizard visits Link on a magical flying carpet to inform the Hero of the dire situation. Only Link, with the aid of the Book of Koridai, can defeat Ganon, so Link willingly boards the carpet, and the two fly to Koridai... Many backgrounds were taken from the Zelda Cartoon and used as backdrops in the game.
Zelda: The Wand of Gamelon
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The King of Hyrule has embarked on a journey to make a treaty with Duke Onkled, but somehow has disappeared en route. Link, in true hero fashion, sets out to rescue him. He also vanishes, and so it is left up to Princess Zelda to save the duo, and to find out why they went missing in the first place.
Zelda's Adventure
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Hyrule is in the middle of the Age of Darkness, as Gannon (in this game it is spelled with 2 "n"s) has kidnapped the Hero, Link, and unleashed his rule over the land of Tolemac. (Which is Camelot spelled backwords) Princess Zelda sets out to save the young adventurer, and learns from the astronomer Gaspra that she must first collect the seven celestial signs before she can conquer the dark king and bring Hyrule to an Age of Lightness.
The story is told mostly through live-action FMV scenes filmed in the Netherlands.
EDIT - The second two games actually play as Zelda instead of Link. It's a great idea, but... They screwed it over.
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