A lot of players concentrate on their characters' strengths, building a powerful caster, an agile sneak-theif, or a brutal barbarian warrior. Equally important though are the flaws in your character. These are generally skipped over entirely in the books, so here are a few examples to inspire you. A hero with problems, in my opinion, is a more interesting character than an alabaster statue. Flaws also, almost more than strengths, open up opportunities for further background development. Without further elaboration, here are a few ideas.
Everybody is afraid of something. Fear of heights, spiders, fire, the dead, darkness, clowns... the list goes on. Beyond these fears, there are subtler terrors in the world around us. Fear of betrayal, fear of failure, fear of capture... these phobias are trickier to role play, but equally fun. What are you afraid of? How did you develop this fear, and are you struggling to overcome it? How? A character without any fear at all can be fun to roleplay as well.
MISSING LIMBS OR FEATURES
Fantasy worlds are dangerous places. It's perfectly reasonable, especially with an older, more experienced character, to assume that some of your past battles will have left their mark. If you decide to be missing a limb, talk it over with your DM. Most will allow it without penalty on a case by case basis, or allow it to be folded into your stats anyway. Maybe your character with low dexterity is missing a finger, or there's a horrible scar marring your barbarian's 6-Charisma face. Have you suffered a grievous wound? How did you injure yourself? What did you learn from that injury?
Not all injuries are physical. Just as a character can suffer violent traumas, magical affects and simple shock can also have lingering consequences. Your character might be OCD or suffer from PTSD. Your mage might have developed a stutter. Maybe your rogue suffered the ill effects of a trap and occasionally hallucinates. Your one-time knight was hit by a powerful enchantment, and now believes himself to be trapped in somebody else's body. Maybe he's right.
Some people are picky eaters. Some have bizarre religious beliefs that limit what they can consume. Your barbarian might come from a culture that accepts cannibalism, or even requires it. Maybe your character is lactose intolerant. Do you drink? Do you eat vegetables, or require particular foods or medication? When you go to a tavern, think bout what you're actually going to buy. What kind of food to you like? Are you accustomed to the finer foods, or do you get what you can as it becomes available?
COMPULSIONS OR ADDICTIONS
Some people aren't fully in control of themselves. They have ticks, urges, or addictions that edge them toward various actions. Schizophrenia would be a good example of what I'm talking about. Maybe you were possessed once upon a time. Are you a compulsive gambler? Liar? Theif? Are you addicted to any chemicals? How were you introduced to them? Are there voices in your head? How did they get there? When they talk, do you answer?