I'd like to be a neutral-neutral paladin...
If I could choose one character that wouldn't make sense in a Dungeons and Dragons atmosphere, it would be a neutral-neutral paladin (paladins are always seem to be good, lawful people rather than neutral).
I know this thanks to this quiz that was brought to my attention by correspondguy.

How evil are you?
I know this thanks to this quiz that was brought to my attention by correspondguy.

How evil are you?
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Glad to know you're a good guy ;).
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That being said, I find neutral characters to be amazingly boring. Most of my characters are female, chaotic, and willing to use their sexuality to an advantage whenever possible.
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When I did play DnD, I liked to play male, lawful characters who naively believed in the laws of society.