Well...Link doesn't actually have a personal personality. I mean his personalities differ, not just because he's different on a handful of games, but also because YOU are Link. You are who Link is! If you like slashing up pots, taking rupees, then you can say Link is a cruel, thieving, destroyer. If you help out Gorons from the pirate's hideout, then you are a kind, brave, young man. It really comes up to you.
Not really, as I said before, quoting Extra Credits, ACTIONS define a character. Primarily actions involving the game's plot.
Like they did with Samus in the "Learning from Other M" video, using events from game plots and what's written and hinted out to give a guess what kind of a person she is, we can do the same with Link.
Here's what we know of him.
We know he's young, usually from 10-19.
He's shown to be reliable when others need, say, monsters in a cavern to be removed.
We know that he can use a sword as well as other weapons needed for his quest, learning what he can when needed
(Apparently he has access to the Autobots' transwarp technology to store them)
In most games, he's orphan, but he always doesn't have his birth parents, which could be a sign of loneliness or understanding the importance of family.
He's seen as a big brother type to kids, especially in Wind Waker where he has a sister.
He's chosen to wield a sword that is the "blade of evil's bane" that no one with an evil heart can use.
He genuinely dislikes those who not only want to rule Hyrule, but endanger lives.
Whoever he is, he's proven he's not only brave enough, but determined enough and competent enough to travel into volcanos, underwater, through time, into the desert, up a mountain during a blizzard, into unknown territory in the skies or even travel from the skies, enter different worlds and face monsters and evil rulers all for not just his friends, but all of Hyrule on numerous occassions.
And we see he has a kind side, since Majora's Mask had him searching for Navi when she left, or his concern for Midna during brief scenes in Twilight Princess, or the mentioned little sister of his in The Wind Waker. And the first game's manual states he has a "burning sense of justice" when he saves Impa and presumably never asks for anything in return.
And some games suggests the kind of relationship he has with Zelda, whether it is acquaintances in Twilight Princess, good friends/implied romance like in Ocarina of Time and SS, or clear signs of affection like in Spirit Tracks.
Sure I might be guessing a little... and I couldn't help but make a jab at the whole weapons coming from nowhere trick, and while he can do minor things like take fallen items or smash pots, that's just minor stuff the player does for fun. It's the major things, like story or sub-plots, that show there's a character with his own personality in there.