The Cupid- Asexual character uses her uncanny familiarity with nonsexual intimacy to set up sexual characters. Character is out, proud and wisecracking ("you look fantastic, now run off and have some of that sex you like so much.")
The Closet Case- character with conflicted feelings about being asexual finds community, wears t-shirts, gets an asexual love interest.
The Asexual Slut- affectionate, flirty, this character gets nonsexually intimate with everybody. This character is out, proud and empowered, she/he has an uncanny ability to turn sexual tension into, a she puts it "something interesting." People who think they are going to bed with her wind up staying all night doing something that they find more interesting and personally relevant than sex, much to their surprise.
The Homewrecker- boy meets girl, girl meets asexual. Boy and girl struggle to understand what constitutes "cheating" when an asexual is involved. At moment of confrentation asexual befriends boy, they figure it out and live happily ever after.
The Clueless- otherwise intelligent character simply does not get sex. Accidentally makes comments with sexual innuendo. Asks for sexuality to be broken down in nonsexual terms ("So what's the deal with butts? Someone break it down for me, I'm lost here.")
The Vis King/Queen- Whenever character mentions asexuality, people around her overreact with confusion. Character is annoyed by this, and has a glib line that she uses to explain asexuality and dismiss disbelief. ("Some people like sex a lot and some only like sex a little, right? Some people don't like it at all.")