I recently started a new character, an Argonian Dragonborn named Claws-At-Neck and he is indeed a very evil character. What I would define an evil character to be is not just a mindless killer. An evil person would for instance decide to go after the Golden Claw, return it only to murder the shop keeper in his sleep, steal the Claw then sell it to his sister as she tries to take over the shop. Afterwards one would murder the sister and reclaim the claw. Leveling up Pickpocket so you can drop poisons in people's inventory is a great way to kill them off silently.
Guidelines for Evilness.
1. Never use any other Speech option besides Intimidate when it is available.
2. Do not give a single coin to beggars, extortionists, or merchants. Steal, barter or sell items for coin that you must keep yourself, exemption for Follower.
3. Responses should be limited to Selfish or Harsh comments, never apologize for anything.
4. Never Yield to a Guard, ever. Either Fight or Flee
5. Become a Vampire and maintain it. This creates fear in NPC's when they see you and makes the game more challenging.
6. Your follower should look evil, if you have one. Deadric armor is great for this look on Warriors, and i personally use Thalmar robes for any mage followers.
7. Come across someone walking alone on the road? They need to die and their items yours. If you have a follower, command them to slaughter the poor soul on your behalf. Once you get to the point you can summon a dragon, well sit back and let your pet feed on a Mill or Mine.
8. Buy the mass murderer's house(Windhelm?) and sadly, clean up the blood stains first before you purchase any other upgrade. This house has the same feel as the Haunted Manor in Oblivion. You get a spacious Lair with secret room to commit evil!