I have an idea.
In Oblivion, there was an Arena to compete in. Players used this arena to fight for "Pain & Glory", but mostly for money. Once the player became champion, a small boy named "Adoring Fan" would follow the Grand Champion, wherever he went. Players had lots of fun taunting and killing this boy.
For Skyrim, I suggest that the adoring fan be avenged. Enter the Bully.
The Bully would be a very powerful "companion". The companions sole purpose would be to taunt the player throughout the game. This bully would not give the player an option, either. The player would not simply be able to kill the Bully without a lot of advancement in Skyrim. If the player got into a combat situation, the Bully would activate an invisibility spell, to avoid combat, so he can continue to jeer such things as "haha you missed!" and "oh THAT was effective...." and "hehe I bet that stings!". Of course, once the player levels up enough, or stacks enough poisons, he/she can choose to eliminate the bully.
Your Adoring Fan,
KSIMP