I get that with the bookmarks icons. My desktop icons are stable.
I'm running 10.04LTS so this may not be where your problem is, it worked for my install:
In "System - Preferences - Appearance - Visual Effects" click the "Normal" radio-button.
If it's already in "Normal", click "None". Restart. Then as above. Then restart. (check to see if it's still as selected.)
If this doesn't help, in a terminal (Applications - Accessories- Terminal) type (copy'n'paste this string):
sudo killall gnome-panel && sudo reboot
It will ask for your password, type it CAREFULLY as it doesn't appear on-screen
then hit return & wait while it reboots.
If this doesn't solve the problem, ask on the help forums, giving your set-up details in the question, e.g.
Ubuntu & hardware details, as exact & concise a description of the problem as possible, any common factors such as the app your using, or how many apps, starting or stopping services, etc. You can post screenshots to the forums as well.
I've just had a look on the forums, but without knowing which distro of Ubuntu your running, it's difficult to offer much more advise. Try what I've suggested, just to eliminate anything simple.