Create or buy a Frenzy Spell of fairly high level (Touch of Rage is a good one) and cast it on someone you want to kill.
Casting the spell on the person is not considered a crime, and it will cause them to attack you, so fighting back and killing them won't be considered a crime either.

This is good for Dark Brotherhood Quests, as it will allow you to do them without upping your infamy.

Watch out for guards if they see you casting that spell.