Not so long ago, when I was young and foolish (pretty darn foolish, actually), I heard people talking about building character depth. Somehow, and I'm not sure how this happened, I thought they meant that to make a complete, realistic character, I had to make them flawed.
I didn't like that idea. What, was I supposed to give every character some sort of personality or physical flaw so that people would believe them? That didn't seem like fun. Why would I want every character in my book to have issues? It also didn't seem that realistic. After all, I knew plenty of people that seemed believable enough (heck, they were real, so they ought to be pretty darn believable) and I didn't think they were flawed people.
Then I realized something very important -- I was wrong. What my characters needed were quirks. They needed to have character traits. Things that would make them different from other people in some way. The reader should be able to figure out who this person is.
For example, one guy I know is, well, pretty much perfect. Near as I can tell, he doesn't lie, cheat, swear, or even blaspheme a little bit. I could list his good qualities, but that would get boring after a while. The point is, he isn't chock full of flaws, but he's still a very interesting person. If you asked me to, I could write a page about him, and I wouldn't have to go on about his virtues. He fences but doesn't compete, is Jewish and observant, and sings. Those things make him different from other people I know.
The trick is to know a lot about your character. You don't need to just know what might be wrong with them (I'm not getting down on having characters with deep issues, because there are people like that, so there should be characters like that), or what's right with them (because not everyone has tons of problems). You should know what makes them unique. Does he always wear the color blue somewhere on his person? Does she have a little good luck ritual that she does every morning?
How do you show your character's individuality?