If you are the kind of person who always likes neatness specially desktop, then here is a small trick for you that will simply remove the Recycle bin icon from desktop.
Follow the steps below:
[Start] [Run] [Regedit]
Registry Key: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\
CurrentVersion\Explorer\BitBucket
Modify/Create the Value Data Type(s) and Value Name(s) as detailed below.
Data Type: DWORD // Value Name: NukeOnDelete
Setting for Value Data: [0 = Use Recycle Bin / 1 = Permanently Delete]
Exit Registry and Reboot
Another Method
start->run->gpedit.msc
-> user configuration ->desktop->remove recycle bin from desktop->double click->change it not configured to enable->apply and ok.
now come to start->run->gpupdate.exe and press enter.
your recycle bin icon is gone from desktop nad you will need to revert your settings for get that back.
after reverting setting make sure to run gpupdate.exe command.