Note: a Windows Live account is now just called a Microsoft account. The account removal link remains the same, however. For the updated instructions, see: http://www.accountkiller.com/en/delete-microsoft-account
This link is different from the Live/Hotmail deletion link, so check what you're doing. By using this link, your complete account will be deleted. If you wish to only terminate the e-mail account, look for Hotmail / Live on this site.