If you're lucky enough to live on property with trees but unlucky enough to have had one of them die, don't consider its death the end.
TreeHugger provides some suggestions for what to do with a dead tree. I particularly like the idea for turning the tree into a place for bees. Mason bees would probably really love it.
The suggestion about making the tree into a bee habitat brings up another important point about dead trees: They actually play a big role in ecosystems, attracting many species with food and shelter. Woodpeckers have lots of fun with them.
In terms of what trees do for an ecosystem, their life has the potential to extend well beyond their time for living. If you happen to end up with a dead tree on your hands or already have one, consider some of the ways you might give it an afterlife.