To kill someone in your dream can represent an anger towards that person you were not aware of. It can also symbolize a lack of control over your emotions. Consider whether you know the person in the dream that you are killing and if so, what aspects of their personality you most associate with them. The dream may signify that you are trying to kill this character trait within yourself.
If you dream about killing yourself, this suggests that you are making some major changes in your life and you feel like part of you is going to be left behind. This could be a sign that you are distancing yourself from the decisions you have made, but it could also be a sign that you have successfully kicked a bad habit.