Non-Canon
The Philips CD-i games — licensed out during a failed hardware deal, disowned by Nintendo, immortal as memes.
Fork point: N/A
The Story Arc
When Nintendo and Philips' partnership on a CD-ROM add-on collapsed in the early '90s, the settlement let Philips license Zelda's characters for its CD-i console. Nintendo's involvement stopped at approving character art. The results — Link: The Faces of Evil, Zelda: The Wand of Gamelon, and Zelda's Adventure — have never appeared on any official timeline, and series producer Eiji Aonuma has said on record he doesn't think they 'really fit in the Zelda franchise.'
They survive today mostly through their gloriously stilted animated cutscenes, which became one of the internet's longest-running meme wells. Non-canon, but not forgotten.
Games, in chronological order
Link: The Faces of Evil
One of three Zelda games produced for the Philips CD-i under a licensing deal struck when Nintendo and Philips' partnership on a CD-ROM add-on collapsed. Nintendo licensed only character likenesses; it had no real hand in development.
Zelda: The Wand of Gamelon
The second CD-i title, and the only Zelda game in which Princess Zelda herself is the playable protagonist, searching for Link and fighting Ganon on the island of Gamelon.
Zelda's Adventure
The third and last Philips CD-i Zelda game, an overhead-view action-adventure closer in structure to the original NES Legend of Zelda, developed independently of Nintendo under the same character-licensing arrangement.