Zelda is a character in The Legend of Zelda series. In truth, like Link, Zelda has reincarnated numerous times over the ages, being irrevocably tied to the very world of Hyrule itself. Although the original Zelda was not of royal blood, she did found the kingdom of Hyrule after Skyloft collapsed to the Surface.
The entire series is in fact named after her, which stood as a state of wonderment and confusion for fans for 25 years until Skyward Sword finally revealed her to be the reincarnation of the world's fourth goddess, Hylia. Despite this, she has only been playable a few times.
Zelda first appeared in The Legend of Zelda: The Hyrule Fantasy.
One of the Princess Zeldas has been known to take the form of Sheik, a male Sheikah likely due to training by her bodyguard, Impa, who was also a Shiekah. This Zelda appears in the Super Smash Bros. series, although later iterations take the visual appearance of the Princess Zelda from Twilight Princess despite the two being very different characters (although, for the record, they are both incarnations of the same individual).