Answer
This question was answered on December 2, 2004.
Much of the information contained herein may have changed since posting.
One way to fix this problem is to reboot. If rebooting isn't fixing it for you, try fixing permissions. If you don't have write permission to your own desktop, you can't move things. If for some reason fix permissions doesn't work, do this (very carefully)
run terminal
type these three commands, exactly as they appear. You will have to type in your password for the middle one.
cd ..
sudo chown -R myshortusername:staff myshortusername
sudo chmod -R 755 myshortusername
this will reset privs for your home folder, to what should be a usable state. (not exactly what they normally would be, but that would take more commands to get spot on) Because of how the finder caches these things, you may need to log out and log back in again to make the changes noticed.