I think the best apologies involve some sort of visual thing as opposed to a character just saying "I'm sorry". Like in Juno when she gets Bleeker her Tic-Tacs or in "Searching For Bobby Fischer" when Ben Kingsley shows up to his tournament and finally gives Josh the certificate he wanted.

http://www.youtube.com/watch?v=V36gt6_uJy4&feature=related

scene starts at the :39 second mark

From As Good as it Gets:


Melvin Udall: I've got a really great compliment for you, and it's true.

Carol Connelly: I'm so afraid you're about to say something awful.

Melvin Udall: Don't be pessimistic, it's not your style. Okay, here I go: Clearly, a mistake. I've got this, what - ailment? My doctor, a shrink that I used to go to all the time, he says that in fifty or sixty percent of the cases, a pill really helps. I *hate* pills, very dangerous thing, pills. Hate. I'm using the word "hate" here, about pills. Hate. My compliment is, that night when you came over and told me that you would never... well, you were there, you know what you said. Well, my compliment to you is, the next morning, I started taking the pills.

Carol Connelly: I don't quite get how that's a compliment for me.

Melvin Udall: You make me want to be a better man.

Carol Connelly: ...That's maybe the best compliment of my life.

Melvin Udall: Well, maybe I overshot a little, because I was aiming at just enough to keep you from walking out.

From The Life Aquatic (I think I'm a little obsessed with this movie right now). And I can't find a youtube video.

Steve Zissou: You know I'm not big on apologizing. So I'll just skip it if it's all the same to you.

Eleanor Zissou: Okay.

Steve Zissou: Anyway, I'm sorry.