What does it mean to dream of your own death?

One of the myths about dreams is that you can’t die in your own dreams…. Anyone who has died in their dreams knows that this is not the case.
The mistake many people make in trying to understand their dreams is to take the dream literally and not metaphorically. That one dreams of a plane crash, for instance, does not mean that one should cancel all plane reservations. The question to ask is, “What is going on in my life that is like a plane crash?”, or “What emotions have I been having that are similar to a plane crash?” (I had a friend, for instance, who dreamed of a plane crash as he was in the process
of getting a divorce.)
Similarly, to die in a dream is suggesting that a part of one’s self is dying or has died. Death dreams are often dreams of transformation; for a new part of the self to emerge an old conception or an old part of the self must die.
Jeremy Taylor, who writes some of the best books on dreams and is one of the best dream workers I have seen (at a conference of the International Association for the Study of Dreams) writes:

Dream Themes:

I Kill Someone, Witness A Killing, or Kill Myself

The central image here is the “death” of those dream characters. No matter how distressing these images are during the dream, they are almost certainly symbolic pictures of ways in which I am growing and changing, ways in which my life energies are being redirected from old attitudes, perceptions, and self-images. In my experience, it doesn’t make a great deal of difference who dies in the dream–if someone or something dies, it signifies that growth and change are taking place. If the dreamer dies, the changes in waking life are likely to be noticeable and radical, and will probably manifest themselves in personality and opinion changes. If it’s someone else who dies in the dream, this suggests that the changes are taking place a little further away from the sense of core self –but changes are happening nonetheless.

Suicide in dreams takes on a particularly ironic and positive quality in this sense; it means that the psycho-spiritual growth and development is taking place as a result of conscious choice and decision. For a person in recovery from addictive behavior, for example, to dream of “suicide” is a particularly positive image, because it usually means that this time, the decision to quit is actually going to stick, and the old, addictive personality really is dying.

from www.jeremytaylor.com