TES games are increasingly forcing players to conform to specific playing styles (in the name of balance) and this is making it increasingly difficult to come up with out of the box character ideas. Some of my most rewarding characters in previous games were:
True Thief (100% non-combat - never killed anything. Ever)
Fisherman (made a living off the seas instead of the land).
Trader/Merchant (inability of Beth to come up with any sort of a functioning economic system kinda ruined this, but i certainly tried, and would like to again)
As for Skyrim, i'm still on my first character, which i don't really consider to be my character at all because he's the Dragonborn and Beth is playing that one for me. The only out-of-the-box concept i've thought of so far is a Miner/Smith (someone who wanders the lands with a pickaxe making a living by selling the items they craft). However, until a mod can do away with the level scaling, such a build would become too difficult to play. I do intend to try it though.