Depends on which icon. A built-in desktop icon like Recycle Bin or My Computer, an icon for a program you installed, or the pesky little show / hide desktop icon in the quick launch area (taskbar just to the right of the "start" button)?
The built-ins can be controlled by right-clicking on the desktop, selecting Properties, going to the Desktop tab, and clicking the Customize Desktop button. This will let you enable / disable My Computer, My Documents, My Network Places, and the Recycle Bin.
Are you the famous Sailbad the Sinner?