This isn't what I personally think about the different Links, but they're somewhat plausible.
OoT Young Link
This little kid is exactly that – a little kid. Really, he'll do anything of what people tell him to do. He has no sense of right or wrong, evidenced by his witless finding the spiritual stones and opening the Door [to Darkness]. As ZeldaOcarina said, he does have basic emotions but he doesn't know how to apply them.
OoT Adult Link
Having spent 7 entire years comatose or near to it, he probably is still somewhat of a child though not to the extent he was 7 years ago. I believe he has a better sense of right or wrong, and ultimately he'll do what is needed of his destiny as a hero. That's not to say he doesn't mess around occasionally; too often has he gone to the Archery Minigame back in Kakariko.
MM Link
A world renown hero, MM Link in my imagination is a cold, distant person. Having seen darkness in the eye, that has likely done a number on his personality. Despite his appearance as a 10-12 year old boy, I'm sure he's adopted the demeanor of an adult, from giving death threats to anyone who gets in his way to doing what seems right...to him. I see him as going in any number of paths; he purposefully chooses to abandon the present to return to the past, just to get a kick out of it. What's it to him, he can replay the events all he likes!
TWW Link
A kid in all respects, after all he IS just growing up.
TP Link
More on the lines of an adult, more adult than OoT Adult Link. He has some obscure bottles in his basement which could mean any number of things. He is seemingly more astute and knowledgable in many fields. Had he chosen to, I'm certain he could become Prince or even King of Hyrule.