My favourite Links are Ocarina of Time's Link and Twilight Princess' Link.
That first one is most likely the one who has the hardest time, not just physically (which is basically the same for all Links), but emotionally. After all, he was thrown from a (guessing here) 10 year-old kid who lived his live without a fairy, being only accepted by his friend, Saria, into adulthood 7 years later.
When he woke up, Link knew nothing of what the world had come to, nor did he know what he had come to. He did not have those 7 years everyone else had... he had changed, a lot. It's a miracle he didn't go crazy. I guess that for him, waking up was like waking up from a coma...
In a way, I think he was really lonely... even more so then when he was a kid. At least then he had steady ground beneath his feet, as an adult he has to struggle to find that steady ground. Get what I mean?
As for Twilight Princess Link... He's the one with responsability. As mitchman said, he has to look after those 3 children... As he kinda promised to search for them and guarantee their safety, even though he didn't knew at that point they were okay... more or less.
He bears responsability for Midna as well (she's no damn imp >:, I like her), when she was hurt so badly by Zant.
And it's just awesome that he can change into a wolf...
(ps, don't go saying that the other links don't bear responsability... Of course they do, for the fate of the entire world of Hyrule (and beyond) rests on their shoulders.. And WindWaker Link bears responsability for his sister... Yet I find it a little different in TP. ^^" )