Paul: If are using KDE it is easy, go to system settings > window behavior > virtual desktops > different widgets for each desktop.
I don't think there is a way to do it in Gnome. I haven't used any other manager enough to know how to do it.
As I thought, ArtistX which is my main OS is based on Gnome.
paul-ax09@paul-ax09-desktop:~$ echo $DESKTOP_SESSION
Disappointing! I've always wanted to have different backgrounds. I think it would be helpful in keeping different desktops for different uses and distinguishing them easily one from another. Never mind, the panel where I switch from one desktop to another has an icon that reflects what is open on that desktop, so I can easily see where my browser is, where my torrents are, where my konsole windows are, etc.
Window selections in bottom panel.
1-Firefox, 2-Chrome, 3-Picasa, 4-Transmission, 5-Nautilus, 6-Konsole
One-click switching between tasks.