The Legend of Zelda
Zelda is kidnapped by Ganon in this game and lets Link know at the beginning of the game. She is rescued at the end of the game after you defeat Ganon.
Zelda 2: The Adventure of Link
Zelda is cursed by one of her magicians and is put in a deep sleep. You save her at the end of the game after defeating Dark Link. This Zelda is the ancestor of the Zelda from the first game.
A Link to the Past
Zelda is rescued at the beginning of the game. She is the last if the maidens that the evil wizard Agahnim needs for his plan.
Zelda is not in this game, however, she is mentioned at the beginning of the game when Link mistakes somebody else for her.
Ocarina of Time
Zelda is first seen as a child in this game. She and her guardian Impa escape the castle shortly before Link is attacked by Ganondorf. She entrusts the Ocarina of Time to Link so that he can protect it from Ganondorf. This was a huge mistake because Link accidentally opened the way to the Sacred Realm. Ganondorf gets the Triforce of Power and tries to find Zelda, but she is disguised as Sheik.
Zelda is only seen in a flash-back where she teaches Link the Song of Time. The flash-back isn't taken from Ocarina of Time, but rather the unseen ending of it where Link starts a journey to find Navi. You could tell because Link is riding on Epona. Also, a little information about that is in the manga.
Oracle of Ages and Oracle of Seasons
Zelda orders Impa to guard Din and Nayru and escort them back to Hyrule. She is kidnapped in both games. Once both games are complete, she is kidnapped by Twinrova. Twinrova is attempting to bring back Ganon.
Zelda is a pirate named Tetra that wears a Triforce necklace. She is discovered by Ganondorf but he is not able to capture her. After that, she finds out her true identity in the underwater land of Hyrule.
Four Swords Adventures
The Minish Cap
Zelda chooses to be imprisoned in a tower by Zant to keep her people safe. She meets Wolf Link in this tower. She is not turned into a spirit unlike the others who became imprisoned in twilight. Near the end of the game, she is possessed by Ganondorf. After defeating her and Ganon Beast, Midna tranports Link and Zelda outside. You fight the final battle alongside her.
Zelda is only shown in the introduction, but she is in the form of Tetra in the game.
Zelda's body is taken by the Demon King Malladus, so she is a spirit inside a knight's armor that aids you in your quest.
Zelda is Link's friend and is not a princess. She is swept off of her loftwing by a tornado, but is rescued by Impa. She gives Link the Goddess Harp before escaping Ghirahim. They both have a secret love for each other.
Zelda is a hylian, obviously, since she's the princess of Hyrule.
Tetra is Princess Zelda's other form from The Wind Waker, Phantom Hourglass, and Spirit Tracks (there is a painting of Tetra in Hyrule Castle). In Phantom Hourglass Tetra is quite annoying.
In Wind Waker, she is a pirate who the mail man of Outset Island blames for Aryll's kidnapping. After you're failure at Forsaken Fortress, you don't see her again until when you get bombs. She saves you the second time you go to the Forsaken Fortress, but her true identity (Zelda) is discovered by Ganondorf when the Triforce of Power resonates on his hand.