Go to "C:\Documents and Settings\<username>" and simply copy (or cut and paste) folders, files, etc... in any of the subfolders into another location on the hard-disc (where <username> is the user account that you want to remove)
Next, go to "Start->Control Panel->User Accounts" and click the username that you want to remove. Click the "Delete Account" option.
Now, finally, you will need to perform this simple tweak:
Click "Start->Run" and type in "control userpasswords2" (without the quotation marks) and untick the "Users must supply username and password to access this computer" option (or words to that effect)
You have now successfully backed up the files from the user account and removed the account from the system