While getting your desktop clean of icons was a minor challenge in the past-- it is almost too easy of a thing to do in Vista. Just select and delete and it is gone. You might just do this accidentally when trying to empty the recycle bin and getting it back was just a little hard to find so I figured it worth pointing out:

Right-click the desktop and choose "Personalize" or open the control panel and select "Appearance and Personalization > Personalization". Now don't get hung up trying to find any help on the right pane where all those helpful applets are described-- this particular setting is at the top left of the window under "Tasks" named "Change desktop icons".

Click "Change desktop icons" and you'll see a simple window to choose what standard desktop icons you may want and even an option to change any of the default icons for those items.