Is there any way to automatically receive an email to myself (the admin of the list) when a new subscriber joins the list?
Not in CM no, You can use the RSS feed and an RSS to email provider.
I'm currently working on a 3rd party app which will do this automatically, but unsure when i'll release to the public.
Hi chad, JonJoyce is on the money here. I've listed a few services you can use to get updates in this blog post.
JonJoyce - keep us posted if you do release this app, we'd love to check it out :)