On occasion Zelda has been known to take on different forms. This will happen for one reason or another. As to what those different forms may be read on.
In The Legend of Zelda: Ocarina of Time this is the first time we see Zelda take on an alternate appearance. When Link's spirit is sealed away in the Sacred Realm for seven years Zelda takes on the appearance of Sheik, a mysterious young man who claims to be one of the last remaining Sheikah, in order to hide herself from Ganondorf. Sheik first appears before Link at the Temple of Time when he is now an adult and explains to him that in order to defeat Ganondorf he must awaken the sages. After that he is seen on occasion, giving Link guidance on his quest and teaching him songs that will allow him to warp to the temples of the sages. Once Link awakens all of the sages the two meet up again at the Temple of Time where Sheik then reveals himself as the princess Zelda and gives him the Light Arrow.
Next is Tetra. Appearing in The Wind Waker and Phantom Hourglass, Tetra isn't really so much an alter ego but rather a raised in a different lifestyle. Still, I thought she was worth mentioning here. Instead of being raised as a princess Tetra was raised as a pirate, likely a result of the great flood that left all of Hyrule under water. Either way though she's not like your average Zelda. While she is still a leader of sorts she is a lot more tomboyish and aggressive than your average Zelda, and she takes no crap from anyone. Despite all that though she has a kind heart. When she learns she is Princess Zelda she is shocked and is told to remain in hiding until Link finds the pieces of the Triforce of Courage but is captured. During the final battle with Ganondorf she will fight alongside Link using his bow and Light Arrows.
Last is the goddess Hylia who appears in Skyward Sword. While I'm not exactly sure you'd call her an "alter ego" of Zelda, as she is the mortal incarnation of the goddess herself, I still thought I'd include her here anyway. When the three goddesses had created the world, the Triforce was entrusted to the Goddess Hylia to protect it. She did so for a good many years until the Demon King Demise had launched an attack in order to take it from her. Many people had died and in order to protect the remaining survivors and the Triforce she sent them to the heavens, away from the evil. She and the remaining five clans then defeated Demise, sealing him away and restoring peace to the land. Knowing he would not remain sealed forever Hylia abandoned her divine powers to transfer her soul to a mortal form so that one day the Triforce could be used. Hylia would eventually be reborn as Zelda but retained no memory of her past life.