For once a simple one! You simply right clight on the desktop and choose the desktop tab after clicking on properties. That will be the second tab next to the "themes" tab. Once you open that click on the "Customize Desktop" button and look at the items seen in the top row. You can even change icons for the full and empty recycle bin as well as uncheck it. There you can make it disappear just as easy as making it reappear. Just uncheck the two!
"Remove Recycle Bin
Posted 8/26/2002 by TweakXP Member
How to remove Recycle Bin Icon from Desktop If using XP Pro
Go to START > RUN
Type GPEDIT.MSC
Navagate to USER CONFIGURATION >ADMINISTRATIVE TEMPLATES >Click on DESKTOP,
On the right hand pane find " Remove Recycle Bin icon on the desktop " , double left click on it to ENABLE it.
Sorted! If using XP Home
Either use TweakUI or make the change manually in the registry.
Create or modify the following registry entry
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\HideDesktopIcons\NewStartPanel
{645FF040-5081-101B-9F08-00AA002F954E}
REG_DWORD
0x00000001" http://www.tweakxp.com/article36805.aspx
One word of caution should be made here if you have never made an edit in the system registry do so at your own risk! Although this one seems easy enough it is also quite simple to "make a goof" in there when trying things out.