A YouTube Help thread have a confirmed bug report that you are currently unable to delete your YouTube account.
The issue first started happening yesterday where users of YouTube who changed their minds and wanted to delete their YouTube accounts were unable to. Typically, you can delete your YouTube account over here and by clicking on this button:
But now if you try it (FYI, I did not try it) nothing will happen.
Brian from the YouTube team said it will be fixed shortly. He did offer an alternative way to delete your YouTube account. You can delete your whole Google account and that would remove your YouTube account - for many that is not an option.
Hi rkgjoiunhgse - unfortunately, there's a bug right now with the account deletion page. We plan to have it fixed in the next day or two. In the meantime, if you created your account after May 2009, you should be able to delete your account by deleting your whole Google Account - if you don't mind losing your Google Account, that is.
Forum discussion at YouTube Help.