To delete a YouTube account, first sign in to your account. Secondly, go to settings and then click on your username. Next, click on settings from the drop down menu and later click on the advanced button close to your picture. Select the 'close account' tab to permanently delete your account. Get more details on http://www.wikihow.com/Delete-a-YouTube-Account.
If you are sure and don't want to open it again. while you are in settings, change your password to some random letters and numbers that you won't remember. Copy and paste the same in the confirm space. Then change your email address to something rediculous like firstname.lastname@example.org. The account is now destroyed and un-recoverable by anyone.