What I want is a mailing list manager that I can install on my site. I want people to sign up for newsletters using a name and email address, and then have that information stored in a file or database. I'd then like to use a backend to manage this list and send emails to people.

Is there a free program that does this without using an advertisement in the footer? Maybe something open-source?

Mailchimp won't cut it and Constant Contact isn't free.