application has expired?

If you can find the name of the application by right clikcing the mouse over the icon you can do one of two things
1. The icon wil also list the location of the icon on your hard disk, so you could map to that area and actually hard delete the whole folder. Then just drag and drop the Icon into your recycle bin
2. You could go through Start/Settings/Control Panel
Then select Add/Remove Software and Uninstall the software this way and it should remove the icon from the desktop as well

Chip
May 2009

It sounds as though your licence for this application has expired, although you don't mention which application it is.

K
February 2009