You can, but unlike in Windows XP and Windows Server 2003, you need to do a little bit more clicking...

Someone in the Windows XP/2003/Vista design team has decided that desktop icons are bad for you. I don't know what this assumption is based upon, but one of the first things I do whenever I put my hands on a computer, any computer, is to add the missing icons. Too many easy shortcuts are missed because of the removed desktop icons, and I'm just too hooked on them to live without them.

So in order to restore the desktop icons you could use just one method instead of the 2 methods in Windows XP/2003 (see comment below).

Right-click an empty spot on your desktop, select Personalize.

In the Personalization window, in the top left-hand corner, click on "Change desktop icons". Note, you can also get to this window directly from the Control Panel.

In the Desktop Icon Settings window, click to select all the empty checkboxes for the desktop icons. Click Ok.

Done.

Note: As I mentioned earlier, in Windows XP/2003 you could use a second method - by reverting to the "Classic" Start menu you got your icons back (but also missed the "Regular" Start menu as a result). In Windows Vista doing so will only return the Internet Explorer icon back, not the rest of the desktop icons.

Bahhh...

Another, more advanced note: If you don't want to go through all the clicking and crap that the Vista inventors have imposed on us, you can simply execute the following command from the Run command:

"C:\Windows\system32\rundll32.exe" Shell32.dll,Control_RunDLL desk.cpl,,@Web

This also works in Windows XP/2003.