All very good responses, and helpful, too. I'll try and respond to some of the individual questions raised.
In general, I'd say there are two aspects common to all characters I play - I tend to gravitate to the 'tragic hero' stereotype (my character backgrounds tend to have enough potential disasters and crises in them to make four or five characters miserable), and I prefer to play something different from everyone else. I enjoy myself less when I play one of two mages in a group, or one of two or three rogues. Generally, this isn't a problem, as our group is fairly good at discussing character concepts before rolling them up, so I have a chance to hear what others are planning on playing. So really, there's nothing here that would be causing a problem, as D20 is as good as any other game system in terms of variety of character types, and the tragic hero part is pure roleplay and has nothing to do with rules.
As far as specific concepts for the current game, to be honest I hadn't settled on one yet, and I was just tossing around vague ideas in my head. Having had more time to reflect on the issue, I think part of my mental block lies in the fact that for a few months now, I've been creating a number of D&D characters without much thought toward developing a personality. After all, these were one-shot games, why bother? So now, my brain is having trouble getting past the assumption of "D20=Two dimensional character".
I'll have to take a look at Scarred Lands to see if I can get inspired; I'm generally familiar with FR so I know what directions I can take there. Some of the suggestions given are good and may lead to inspiration (which was partly my intent to begin with).
A specific comment to Dareoon; I think your summary is close, but not quite there. The best analogy for my situation I can think of would be like this: Imagine that every night you got chicken for dinner. Now, you like chicken, and it's prepared well every time, so that's not a problem. But at the same time, the person serving your chicken dinners keeps mentioning that in a couple of months, you'll be getting beef instead of chicken. You don't really have a preference for beef over chicken, or vice versa, so you keep eating your chicken, but in the back of your mind you're thinking about beef. You think about what kind of side dishes go with beef, or what kind of wine goes with beef. So a couple of months go by, and the chef announces he's going to put out a new menu. When he does, you discover that all the dinners for the next year or so will be... chicken. Even though in the end you like chicken, it can be hard to shift expectations.
(So, anyone hungry yet? I think I'll go make pork chops...)