I find that having a rich backstory for my character isn't enough for me anymore. I need to find something that gives the character some uniqueness. For example, I'm thinking of creating a savage bosmer, fashioned a bit after american indians, who takes reverence of nature to the extreme and will slay anyone that harms it in any way. He respects the green pact even outside valenwood so he only uses animal parts for his alchemy. That's unique enough to change the gameplay in a pretty drastic way.
I also read some months ago of a player that had a sage character; he collected every book in the game and read them all in his endless pursuance of knowledge. That was his raison d'être. I'll definitely give that a try, once magic is more fleshed out (hopefully in hearthfire!).
I'm wondering if anyone else has characters with unique characteristics that alter the gameplay radically.
Not so much as yours, but the only particularly interesting character I have made was very similar to what your thinking of. He was a Bosmer with war paint who I decided to only let use Fur Armor and Bound Bow with the smallest shield I could find (something like a buckler - Bloody Targe in the end - was restricted to Xbox 360 at the time) and would tank while his conjured minions killed things. He was basically an Apache of sorts crossed with a very hardcoe Bosmer to the point I wouldn't harm wild life (got interesting when I'd get chased by a pack of Bears and Sabercats

).
Now I'm on PC I think I'll give him another shot with mods this time, hopefully make wildlife friendly to my character (if you know any mod that does that, I'd love to know)!
That Bosmer idea was a pretty good idea I'll have to give it a go

Personally though as close to that as I come is including a " kink " in my builds armor/defenses. For example if I'm making a warrior class ( of any sort ) I'll include a " kink " in his/her armor/defenses, I'll make them weak to magic in general or a certain destruction magic ( seeing how this is pretty much all NPC's use ).
The olde combat triangle eh

. There is a mod that alters combat to the point where arrows do more damage to mages in cloth and magic does more damage to warriors in armor (cooking them alive, using their own armor as an oven kind of thing), you should check it out.