I like the idea of negative traits, too. In the Arkania games, you can make your characters claustrophobic or necrophobic. I love the idea of a cleric whose job it is to go into crypts to smite undead actually being terrified of crypts and terrified of the undead.
I'd say there are traits which are simply modifiers dressed up with some flavourful text (e.g. "Zealous: Immune to fear effects when in sight of a church or shrine to your god.") and then there are ones that add totally new things (e.g. "Intuitive: Dialogue options that would cause an NPC to agree or disagree with you are marked in green and red text respectively.") The first ones are easier to implement but the latter ones are a lot more interesting, even if they don't necessarily give you any advantage.
I'd like some characterful things that don't really do anything stats-wise, myself. Things like making your character sing certain songs if he or she gets drunk, or something like "Impulsive", where your character has a chance to randomly choose certain dialogue options without your input.