Wait, what? "Ovarina of Time?" I can't stop laughing at the typo up in the poll. It made me think of "ovaries" which means that maybe that's a secret Zelda game that's either all about Zelda's quest to concieve a child or about Link dealing with cuccoos and their ovum (eggs).
It's hard to say for me. I really like all of the Links.
LoZ Link: My first! He's a cute little sprite and very rough-and-tumble. His quest takes inguenuity and toughness.
AoL Link: He's the same as the first, only older and fighting to claim the Triforce of Courage. He's also an arch-mage - the most magically-endowed of the Links, and that is awesome, especially when you can turn him into a little fairy.
A Link to the Past Link: Such trauma he experiences! His dying uncle, girls telepathically talking to him in his sleep... having to kill Hyrule's finest... but he has a good heart, as shown by his cute bunny form and the wishes he makes on the Triforce. He's an even more adorable sprite than the original! Long live pink hair!
Ocarina of Time Link: Ah, the Hero of the ovaries! Er, ocarina. Good-looking enough in his adult form that many a fangirl would declare him for that typo... I like him a lot. He makes great fanfic writing material because his life is full of conflict (and not just the monster variety). His life is like a trauma conga-line, poor guy. I relate to his "outsider"-ness a lot, being that "kid who never fit in with the other kids." Then the time-travel/coldsleep stuff happens and those things are always interesting to me. I interpret him, in adult form, as "maybe just a little more grown up inside" to match his body, but "still very much a child soul inside a man's body." (Again, I actually feel that way about myself, replace "girl" and "woman" where appropriate, and I've actually *lived* my years...)
This brings me to...
Majora's Mask Link: He may look like a cute little kid, but that's a battle-scarred war veteran's soul in there. He means business and takes care of it. He takes what he must do well, it would seem... it's a game to us, but if any of us were in his position, I don't think sanity would be ours after the whole mess. Again, the poor Hero of Time's life is like a trauma conga-line.
Oracles Link: There's not much to say about him other than sprite-cuteness and that adorable way he falls down when you get a Game Over. I like his in-touchness with Nature in those games, and his ability to put up with crazy Subrosians and Tokays.
Wind Waker Link: Cuteness, energy/excitedness, the comedy he brings to the series. He also is, as mentioned, not a bloodline Hero. He had to proove himself by hunting down the Triforce of Courage. He's also the best big brother any kid could ask for. He may be sweet-looking, but he's got an awesome grit. I've also seen a fan artist (in describing their picture of little Link stabbing Ganondorf in the head as what happened in the game) describe him as the most bad-a$$ of the Links. "Crowning" Ganon was a crowning moment of awesome for him. (I've found that I like playing him an inordinate amount in Brawl).
Haven't played any Four Swords, but I read the manga once when it was available online and found the disperate presonalities and how they fought funny.
Minish Cap Link: Eeeny meeny mini tiny Link! Squee! That is all. I gave him the title in one of my fanfics of "Colossus-Slayer" because of how he had to face big Chus and the Octorok and stuff.
Twilight Princess Link: (Actually is probably my favorite Link. I seem to go back and forth between him and Ocarina-Link). He's a bad-a$$. He's a country man with a simple, tough job - I've worked on ranches, myself - the helpful role-model of his village, and possibly the most realistic of the Links story-wise for the games. Think about it: Ocarina of Time Link was a feral child of the forest and immediately knew how to use a sword and ride Epona. TP Link had apparently had his Epona for years, was again, a wrangler for his village, and was taking sword-training from the town's master swordsman. As a hero, he makes sense.
Haven't played Phantom Hourglass and Spirit Tracks yet.
Skyward Sword Link: The most expressive Link yet! It's like Nintendo took TPs Link's maturity and realism (Skyward was taking sword lessons as part of knight-training, and presumably some other combat and rescue training, he had a lifelong/long-term bond with his steed-creature) and combined it with Wind Waker Link's expressiveness. He doesn't quite have Wind Waker Link's energy, though. I really enjoyed the humorous play on Link's "laziness" in this game, with the ability to put him to sleep if he sat too long. He's great overall at being more "his own character" than player-avatar.
So, yeah, I really like them all.