The Legend of Zelda has mainly been about the single player campaign of travelling through dungeons and defeating the grand villain, however there has also been a few multiplayer implementations in past Zelda games. Four Swords is the most notable example of which four Links were used to go to a quest together via the use of different players. The DS games also received the multiplayer experience which was more of a battle experience rather than co-operating in a quest.
However with the recent two-player co-op in Hyrule Warriors, perhaps the upcoming The Legend of Zelda game on the Wii U will also receive similar experiences…
“The two-player functionality of Hyrule Warriors is actually something that has traditionally been done in the Dynasty Warriors series, but they’ve changed because of the hardware and the second screen on your GamePad. Instead of having a splitscreen on the television, you have one-player playing on the television and one on the GamePad. When I was talking back about making Zelda more than just a single-player experience? That’s something you will see in the future, maybe next year.”
-Aonuma, Gameinformer interview.
I’m doubting that this will be implemented in the actual main quest of the upcoming Zelda game, but perhaps during the development time, by next year Nintendo could announce additional side quests including a multiplayer experience? Time will only tell!