With all the changes happening with YouTube recently, many things have changed, especially being able to delete a YouTube Account or YouTube Channel.
I did create a video on this topic a few months ago, and within a week of me uploading it, everything changed. So this is the April 2014 update on how to delete a YouTube Account or Channel.

The first thing to do when you’ve decided you want to delete your YouTube Channel is to remove or back up your videos. Once you’ve deleted your account, your videos will no longer be available on YouTube, so you won’t be able to retrieve them in any way.
By deleting your YouTube account, you will lose all Subscribers, Views, Videos, etc from your YouTube Channel. So make sure this is something you really want to do.
To delete your YouTube Channel, you have to delete your whole Google+ Account. This will delete your Google+ Page, anything you have in Picassa and anything in any other Google property.
The only thing you don’t lose is your Gmail account. You will still have that when you delete your Google+ Account.
Once you’ve done all your backups and you’ve decided you want to delete your YouTube account, then click on your name on the top of the page – once you’ve logged in of course – and click on Settings under Google Account.
Scroll all the way to the bottom of the page where it says Disable Google+ and click on “Delete your entire Google profile here.”
Check the box marked “Required” and click on the blue button Remove Selected Services.
It will then tell you “You’ve successfully deleted Google+ and all associated social content”.
They will ask you why you wanted to delete your account. You can add some feedback if you want, it’s not necessary.
As I mentioned, you still have access to your Gmail account, if you set one up on the account, and you can use that still.
You can set up another Google+ account and YouTube channel on that email if you wish, at any time.
That’s how you delete a YouTube Account or delete a YouTube Channel.