Even though Star Wars is an unrealistic movie, if you think Luke acts like a real life person would in his situation (which he does not) then you can mention him. All movies represent fake situations, but sometimes an actor will make a character appear to act the same way that some genuine person would act in his situation.
I can’t think of any worth mentioning now, as I wrote this more interested in what Dopers would think. I might post later, after I give the question more thought.
Okay, this is TV, but I’ll say it anyway. The thing that totally struck (and delighted) me about Six Feet Under is the fact that the characters are so completely true to life–they are unpredictable, multi-dimensional, and above all realistic. I’ve not encountered a TV show that has characters more realistic than this one.
As for literature, I think most of the characters in Philip K. Dick’s books qualify. They are the total antithesis of most SFnal characters–not grandiose heroes, not degenerate villains, just ordinary average people. They are neurotic and mercurial and don’t always do “the right thing.” I think PKD’s ability as a character creator is vastly underrated.
Three come to mind right away for me.
In the movie You Can Count On Me, the characters of Sammy (Laura Linney) and Terry (Mark Ruffalo) portray two siblings, and they strike me as being two of the more “real” characters I’ve seen on screen.
In St. Elmo’s Fire, Andrew McCarthy plays a guy who’s in love from afar, and gets love and sex confused. And I think he gets less credit than he deserves. It’s a situation that many people (myself included) have been in, and I think that he illustrates it very well.
I have always thought that Toni Collette as the mom in the Sixth Sense was great. Actually any movie where she’s a mom because I liked her as a mom in About a Boy. Playing a mom on film or tv isnt that easy, Carol Brady is the fakest mom imho, I dont know why people make her out to be an uber-mom.
Anyway Toni Collette as a mom. 
It might not be fair to say this, but I think Raskolnikov in “Crime and Punishment” is very realistic.
I say this might not be fair because:
I don’t really know what it’s like to be a murderer whose conscience is eating him away.
So much of the book is about his overall psychology, so he’s easier to relate to. In a movie, even if a character is well-acted, there’s less of a chance to see what’s going on inside his head.
Still, as I was reading “Crime and Punishment” I was amazed at how convincing his actions and words were. They rang very true. If it’s not realistic, Dostoyevsky still deserves credit for making it seem that way.
After some thinking I’d say Dave Eggers in A Heartbreaking Work of Staggering Genius by Dave Eggers. Yes it is sort of about himself, but it is still fiction.
Lester Burnham (Kevin Spacey) in American Beauty and Nick in Roger Dodger.
I second the two siblings in You Can Count On Me.
Yeah, I agree with the dead author, what about Ulysses?
I was thinking Raskalnikov as well. Or the main character in Joyce’s “Araby”. Little groveller.
Well, if it weren’t for all those convenient Deus Ex Machinas… 
Philip Carey.
You know what kills me about Six Feet Under? The characters have a limited warddrobe. They wear the same articles of clothing multiple times. I can’t remember ever seeing this in any other show, ever. That alone seals the “realistic” deal for me.
Really??? I thought that Nick Cage was completely fake, phony, and unrealistic in that. Then again, maybe it’s because I hate Nicolas Cage.
John Updike’s Rabbit Angstrom?
You mean the Lester Burnham who was obssessed to the point of distraction with the nubile Mena Suvari only to turn down her naked, virginal offer? Possibly the last straw in a movie filled to the gills with contrivances. If that movie had any balls, he would’ve slept with her…
Yes, he has realistic desires and the movie was not afraid to show them. Everything else he does lots of normal people also want to do same things. Smoke weed, work out, have little responsibilities, have sex with teenagers and to tell off your ungrateful wife. The fact that most people can’t find the courage to do these things does not take away form the realism in these desires.
Maybe it would be more realistic if they made a movie where Lester just thinks about all these things but does not do any of them.
I’m willing to let the his turning down Mena Suvari slide since no other movie (to my knowledge) shows a normal guy doing or even thinking about doing the things that Lester does.