Gannondorf the thief is the primary antagonist in the Zelda series of games. Although the story is constantly rewritten with each new game, here goes...

The Legend of Zelda: Although never really referred to as Gannondorf, Ganon, the master of evil, was your primary foe. He stole the Triforce of Wisdom, broke it into 8 pieces, and kidnapped Princess Zelda, to boot. The only weapons which would kill him were the Magic Sword and the Silver Arrows.

The Legend of Zelda II: Link's Adventure: Not the centerpiece villan this time around, however, as the legend went, if you sprinkle the blood of Link over Ganon's ashes, Ganon will be reformed. So, you know, don't die.

The Legend of Zelda: A Link to the Past: This is where the meaty bits come in. Gannondorf was a normal thief until he stumbled upon the Triforce. The power of said Triforce granted the wishes of whomever touched it, granted according to the person's heart. Under Gannondorf's evil heart, the Dark World, an evil parody of the Hyrule Kingdom, was formed. He was then known as Ganon, the master of evil. Hit him with the Master Sword and shove a few Silver Arrows up his ass, and he dies.

The Legend of Zelda: Link's Awakening: He ain't there.

The Legend of Zelda: The Ocarina Of Time: Start over. The Gerudo, a tribe of almost entirely female thieves, had a legend that every 100 years, a male Gerudo would be born (Not entirely sure how he's born outside of artificial impregnation, but just work with me here), one that would be the leader of the Gerudo. Gannondorf the thief was this male. His evil ways led him to the legend of the Triforce. He followed Link into the Temple of Time, stole the Triforce, kidnapped Princess Zelda, and turned Hyrule into a kingdom of evil. Seven years later, Link came back (After being locked in time) with a vengence.

Gannondorf, using the power of the Triforce, became Ganon the demon after Link applied some Hyrulian whoop-ass with the Master Sword and the Arrows of Light.

The Legend of Zelda: Majora's Mask: Not in it.

The Legend of Zelda: The Wind Waker: What's this? Continuity? Of course! See, after being locked away back in Ocarina of Time, Ganondorf eventually broke free and started up some good ol' havoc once again. Got away with it for a while, too. Hundreds of years, in fact. So long that the battle Link had with him was a legend (ignoring the fact that Princess Zelda reset time after it was all done). So, what's a hundreds-of-years-old Gerudo to do? Of course! Try to get the pieces of the Triforce back and become all-powerful!

(Given how the game is fairly new, I won't go into too much more detail so as to not spill spoilers all over the place)

SOURCE: My own memory.