Here are some of the things I do or don't do when roleplaying certain character types (in an attempt to make the game more interesting):

*please reply if you have more suggestions like these

• Classic Thief- never kill anything, never buy anything
  
• Barbarian-never use magic, never sneak
  
• Mage- never use any type of weapon
  
• Bard- oh wait, I would NEVER play a bard
  
• Ranger/Archer- never fast travel
  
• Vampire-never go out in the daytime hours
  
• Assassin (or other evil character)-never do quest where you help others

I played my last character as a permanent level one - something I read in this and the Steam Skyrim forum.

No assigning points to health, stamina, and magicka when you level up.

This also means no skills and perks can be used. You will still level up in skills, but without the skill three and perks, it's a big difference when you're playing.

Live off the land by getting gear from kills, loot or chests. Or purchase from a trader, if necessary. My assassin mostly wore light armor, but had to use 2 pieces of heavy armor because both had a +15% damage to bows.

Finished the entire game that way. Actualy, it was very enjoyable, especially not having to put much thought in which skills/perks I wanted to use.

I just played my version of a pure thief

I can fight if I'm trapped/surrounded but I prefer running
I carry 60+ paralysis poisons for escapes
Used illusion spells to calm/start a riot
Made a list of "most marketable houses/businesses" to rob
Never kill a member of marked house
Follow the advice of shadowmarks

I tried a pure rogue in that I never added a perk to anything but the Thieving skills. Ending up not working after about 15 level due to the fact that there are no Thief weapon skills and regardless of how much poison I used (I could perk Alchemy) creatures were just tearing me up. This might work if you get your sneak up to 80+ or something, but in that middle ground where you can't hide and can't do enough damage it's all but impossible.

Does a nord that only punches things count?