Gnome, hide desktop icons
On a Debian box, before proceeding you have to install the gconf-editor package (if not already done)
#aptitude install -P gconf-editor
now go to Applications->System Tools->Configuration Editor. In the application appeared navigate through the tree to /apps/nautilus/preferences and check (or uncheck) the show desktop option. This will show (checked) or hide (unchecked) desktop icons.