Hmm... interesting question. I've played many Zelda games, but since I've only completed 2 games- Twilight Princess and Ocarina of Time - I guess I can only pick from those 2 games. =3
Let's see... If I could be a male, I would choose either Sheik (if you count him as a boy), or Link. Sheik would be a cool character to be, because he's so mysterious. I personally like being mysterious >=D Not only that, but he's quick. You see the way he throws that deku seed or whatever it is, then dissapears in a flash. That would be sweet! He also seems pretty knowledgable. And talented at the harp.
I guess I would like to be Link... only if I didn't die XD I'd be cool to be the 'Hero' and save the day, sword fight, get cool weapons, meet new people, explore new lands... yeah, I could see myself doing that.
If I were to be a girl, I would choose either Ashei, Princess Zelda, or Malon. Ashei and I seem to have the same sort of personality. Not to mention she has cool armor. I think part of the reason I would like to be her is she sees you off to Snowpeak. I loved Snowpeak. The music was so cool, and I loved the snow. Ashei seems to be a cool explorer and I like her character.
Being Princess Zelda would be cool, minus the whole being kidnapped and possesed thing. I doubt I'd make a good princess, though, hehe. But she seems to be pretty awesome with a bow and those light arrows, and seems to be pretty smart. She has the triforce of wisdom, so that's pretty cool.
Malon would also be a neat character to be, because I've always wanted to live on a farm. That's pretty much the only reason I'd like to be her. XD