- Open Terminal, found in /Applications -> Utilities, and then type sudo mv /System/Library/CoreServices/Finder.app /Applications/ -- this will move the Finder into your Applications folder. (You will be prompted for your password.)
- Still in Terminal, type killall Finder -- this kills the process named Finder, and it should not restart! Note that this does not affect the Dock or Exposé.
sudo mv /Applications/Finder.app /System/Library/Coreservices/
This will move the Finder application back to its original location. After logout, it should be automatically started again on the next login.
[robg adds: Just after 10.0 came out, this hint explained how to replace the Finder with any other application -- I'm not sure if that still works or not. Somewhat more recently, this hint explains how to fully replace the Finder with Path Finder.]

