According to the World Health Organization, about 15% of the world's population lives with some kind of disability. With numbers like that, any kind of media worth paying attention to should have some decent representation of disabled people. Luckily for anime fans, there are some wonderful characters who fit the bill.
Some anime that tackle disability do it with nuance and specificity - if you watch Prince of Tennis, for instance, you're going to learn a lot about Guillain-Barré Syndrome. If you watch Gangsta, you're going to learn something about how real people deal with being deaf. Other anime is more vague about it, giving their characters unspecified injuries or heart problems with symptoms that don't quite add up - but these characters can still tell us important things about the social and emotional implications of disability.All of these characters are an important part of their story, sometimes because of how the show handles their disability, and sometimes because they're just really freakin' awesome characters. See if you find your favorite, or maybe find someone new.
Edward Elric, star of Fullmetal Alchemist and Fullmetal Alchemist: Brotherhood, lost an arm and a leg while attempting to bring his mother back from the dead using alchemy. After getting over the initial trauma, Ed learns to use mechanical limbs, becomes a state alchemist, and is eventually instrumental in saving the world.
At age three, Ukitake (on Bleach) was diagnosed with a potentially fatal lung condition that resembles tuberculosis. While this disease still causes him serious pain and suffering, this doesn't keep him from functioning as a valued member of the Soul Society.
In fact, it's because he tried so many different medical treatments to heal his lung disease that he gained invaluable healing techniques that helped his comrades get through a violent war.
One Piece's Shanks got his arm bitten off while rescuing a very young Luffy from a sea monster. He brushes it off as being "just an arm" and continues his pirating activities as if nothing had happened.
Shanks is actually known more for his bright red hair color than for his missing arm, which is a reflection of how common injuries like this are for pirates. It's also an inspiring that he's so badass, no one treats him any differently because of his disability.
Ayase Shinomiya, one of the protagonists of Guilty Crown, lost the use of her legs sometime prior to the start of the series. She hates being pitied for this, going so far as to beat someone up for suggesting that he didn't want to cause trouble for her because of her disability.
She's proud of her condition, claiming that her wheelchair is what makes her unique, and that her only real disability is dealing with other people's ignorance. You go, girl!