I’ve never kept many icons on my desktop, and tonight I decided to reduce the number to zero. Deleting the recycle bin icon took a little research.
Windows Vista will let you simply delete the recycle bin but other versions of Windows will not.
On Windows 7 you can right-click on the desktop, select Personalize -> Change desktop icons, and uncheck the box for the recycle bin.
On Windows XP, you can edit the registry as described here. The registry changes will take effect next time you log in.
If you don’t want to edit your XP registry, you can right-click on the desktop, select the Arrange Icons By menu, and uncheck the Show Desktop Icons menu. However, this will hide all icons, not just the recycle bin, and will not let you see anything you drag to the desktop until you re-check Show Desktop Icons.
If you miss the recycle bin icon, it’s still in the file explorer on the left side.