What makes a character compelling?

Some people struggle with characterization. I've seen people work on creating characters for years, and never quite master it, and for the life of them, can't figure out what they're missing. There's no magic formula, of course, and I'd be lying to you if I said I knew the answer.

However, here's what I do to create interesting, compelling characters that readers want to read about. They may hate them or love them, but they'll keep reading to learn more about them. Take this however you like; it's not a bible, it's just what I do. People tell me I have interesting characters.

1. Mystery: Don't tell everything about your character up front. If your readers learn everything there is to know about your character in the first chapter, what reason have they to continue reading? But YOU should know. Don't tell all, but know all. It'll come through in your writing.
   
2. Change: The best characters aren't static. Sometimes they start out innocent, and grow into maturity and disillusionment. Sometimes they start out evil, and become good. However, it's fun to play things in the opposite end of the spectrum. Look at Saruman. He was once good, and became a compelling character because of his corruption to evil. The person holding the chalice at the end of the story shouldn't be the same person who set out in search of it at the beginning. Sometimes, a lack of change can be interesting: a character who refuses to change in spite of travails can be fun... as long as they're not perfect to begin with. Which segues into our next criterion:
   
3. Lack of perfection: Perfect people are perfectly boring. Look at your characters, and tell me what's wrong with them. Nothing? BIG problem. No one wants to read about perfection. People who look right, act right, and do everything right make you want to punch them. Give them flaws. I mean real flaws, too. "She can't be mean to anyone, ever" is not a flaw, it's a virtue in disguise. Make them petty, jealous, unable to see the evil in others, whatever. Make it a serious enough flaw that it's going to cause them real problems.
   
4. Challenges: if your character doesn't face genuine challenges, that require sacrifice of some sort to overcome, then they're too perfect. They shouldn't meet all challenges with heads held high, and pass with flying colors. Grind their noses in the dirt. Make them suffer. Make them curse the gods for ever letting them be born. It is from such adversity that true heroes are born. What makes Frodo a hero isn't that he succeeded at a challenge... it's that he went on even through great hardships, unbearable loss, and certain failure. He paid dearly for that moment, and it scarred him forever.

I think the biggest problem people have with characters is the fear of letting go. They invest so much in a character that they really don't want to hurt them, so they can't quite bring themselves to really do so. Which results in a boring story. The Lord of the Rings wouldn't have resonated so much had the characters not truly suffered. And if you'll notice, the ones who get lost are the ones who suffered the least, or in the most superficial ways.