For examples of this phenomenon, I present to you a) Tohru from Fruits Basket and b) the titular character from House.
a) Fruits Basket
There's this trope called the Stepford Smiler where a character seems cheerful and all, but is really masking a deep-seated pain or crazy or whatever. The thing is, no one ever seems to see through it except the audience. The rest of the characters remain painfully oblivious until something happens that causes the mask to break.
Exhibit A: Torhu Honda
Just look at those big eyes and bright smile. So cute! She's kind, caring, unrelentingly cheerful...
But then she's so accommodating that she's practically a doormat, has deep-seated self-esteem issues (as does everyone in the show) and just generally has quite a few sucky moments in her past. Yet, the other characters would never have known if there weren't moments where she breaks down and says something she doesn't mean to. No one; not her friends, not her adoptive family, not even her real family. The audience sees it more than the other characters do, because we see her at her most vulnerable.
Contrast this to:
b) House M.D.
Exhibit B: Dr. Gregory House
Bitter, sarcastic, drug-riddled... He's a bit of a mess.
And everyone seems to know why. Patients he's only just met are monologuing at him, telling him all the reasons for why he acts the way he acts. Sure, sometimes he himself tells us about his past, but it's because people have been poking at him, prodding at him, explaining to him (and via him, the audience) why he acts the way he acts and how beneath his jerkish exterior there is a heart of gold.
I picked these two examples because they are particularly egregious. As mentioned, House's patients almost always seem to know exactly what his game is after just meeting him, and Tohru goes for a long, long time without anyone noticing that she was, oh, living in a tent, abused by her family, blah blah blah. In fact, she has to tell them mostly or have people see it for themselves. And the reverse is true in both examples as well: in early seasons of House M.D., no one seems to see how messed up Cameron is and all through Fruits Basket characters are explaining other character's issues to each other in response to bursts of temper.
And it always seems to be this way. If a character is a jerk, another character almost always has to insist that there is actually some sort of good in him and it will almost always turn out that there is. But if someone is indefatigably happy, it could be anything really hiding under the smile.
It's like characters (and I guess people in real life too) would like to think that when something seems all right, it is, but if something seems to be wrong, we have to pick at it until we find an answer.
Any other examples you guys can think of for either extreme? Or, conversely, any examples that completely defy these generalizations?