Link and Zelda are close friends in The Legend of Zelda: Skyward Sword. Perhaps even more than friends. There’s some romance with the two during an early portion of the game, which was shown in one a trailer (below), and it gives you a very good idea of the kind of relationship they share.
This romance between Zelda and Link almost didn’t make it into the game, however. Director, Hidemaro Fujibayashi, and another member of the development team wanted to include it, but Zelda series producer, Eiji Aonuma, felt that there were already too many cutscenes at the start of the game. Aonuma also wasn’t sure that “lovey-dovey” was the right direction for The Legend of Zelda.
Ultimately, though, Fujibayashi pushed to include the aforementioned scene, and the team decided to shave other scenes off the start of the game to help bring the amount of cutscenes down. The reason they specifically wanted to include it was that they wanted players to have strong feelings for Zelda from the start of the game, which would help them relate to Link’s search for her after she’s taken away.
Something else the team envisioned while fleshing her character out was what Zelda would be doing while you were searching for her, even if these events weren’t depicted in the game. Developing her character further was meant to make the player think about her in a similar fashion all along the way.
Aonuma, too, agrees that the romance between the two characters was the right decision, and himself played a large part in fleshing out the drama at the start of the game. Skyward Sword’s Zelda is described as being bright and mischievous.
