Dark Link is a doppleganger of Link that appears as an enemy in many The Legend of Zelda games. The various battles with Dark Link are often thought of as the hero Link overcoming the darkness within himself. He is the second most recurring villain aside from Ganondorf/Ganon.
This history of the Dark Link entities is organized into the latest "official Zelda timeline", this may change completely in the future as the timeline given is merely meant as an example, and their have been official timelines before it.
The Unified Timeline refers to events before the split in Ocarina of Time and thus occurs in every timeline, the split happens in the final battle with Ganon.
Ocarina of Time
Dark Link appears in Ocarina of Time as a mini-boss in the Water Temple, as he was sent their by Ganondorf. Here he copies Link's attacks move-for-move.
In the manga, Dark Link comes out of the well in Kakariko Village and attempts to kill Link, he is able to match Link bit is defeated after Link uses a new skill, the two then have a horseback battle, with Dark Link using his own Dark Epona. Link and Epona manage to defeat Dark Link and Dark Epona after a brief battle.
This is the timeline where Link was sent back to the past and was able to warn the Royal Family of Ganondorf' treachery, leading to the events of Twilight Princess' backstory.
He also makes a small cameo in Twilight Princess in a flashback, where Dark Link is used to represent evil beings named the Dark Interlopers. It is unsure if they seperate entities or the same being.
This is the timeline where Ganondorf was sealed after ruling Hyrule and then being defeated by Link, he eventually escaped, leading to the backstory of The Wind Waker.
Dark Link appears after Link manages to get to the end of the Take 'Em All On game in Castle Town. He attacks using a copy of Link's sword, bombs, and Bow & Arrow.
This is the timeline where Ganondorf killed Link in his final battle with him, leading to the Imprisoning War described in A Link to the Past's backstory.
A Link to the Past
After braving the Palace of the Four Sword and destroying the four enteties guarding it, Link faces off against four Dar Links which each where a different coloured tunic: Green, Orange, Blue, and Purple. After they are defeated, the curse on the four sword is broken.
Oracle of Ages
Four Dark Links are created by Veran in the final battle against her, these Dark Links do not attack and die in one hit, though they are dangerous obstacles they move opposite of Link.
He is a boss in the event "Link's Adventure" in event mode in Super Smash Bros. Melee albeit completely black and is an alternate costume for Link in Super Smash Bros. Brawl. In Super Smash Bros. Brawl, Dark Link is one of Link's alternate costumes.
This time, he takes his appearance from The Legend of Zelda: Twilight Princess where he has more detail and red eyes. Dark Link still appears in an Event, where Link has to fight him once again. This time, they fight in a Stamina match on the Bridge of Eldin, and have 200 HP each. One of Toon Link's alternative costumes is a Dark Toon Link.
Other Dark Links
Several other beings similar to Dark Link, but also quite different, have appeared throughout The Legend of Zelda series. The first is Link's Shadow - a predessecor to Dark Link who appears as the final boss in Zelda II: The Adventure of Link, and the second is Shadow Link - manifestations of Ganondorf's evil thoughts who appear in both The Legend of Zelda: Four Swords Adventures, and The Legend of Zelda: A Link Between Worlds.