If your computer was lost/stole, I would dissasociate that iTunes machine and change my Apple ID password.
but if you really want to cancel your account...
It's amazing but you cannot cancel an Apple ID. You can call support, but they cannot cancel an account! Dissassociate it from iTunes. Any purchaces on the account will be lost. Delete all personal information and any alternate email address. Next save.. now for the last step, change the primary email address to @noemail.com or something. This will change the Apple ID. Once you logout, the account will essentially be gone. To gain access, use the fake email and your password. Since the email won't verify, you will need to change it to a real email and verify if you ever want to regain access.