How do I set up my WordPress Blog so that when a user Registers, the notification goes to me instead of to the user ?

I am told that should already be getting such notifications. They are sent to the email address configured under WP-Admin -> Settings -> General.

But when someone registers and creates a new account, doesn't it go to the user's email address for verification?

I get notifications that comments have been made. Do I also automatically get notifications when a new user registers?