No! You only need your own domain name. Most small domains do not run a mail server, but instead contract out for web/email hosting services at a hosting company such as Interland, Hostway, Glob@t, etc.

When you sign up for the SpamStopsHere service, we email you a list of the changes that need to be made to your domain's DNS MX records. Some hosting companies let you change your own DNS settings through a control panel. Others require that you submit the requested changes to their technical support department. Within a few minutes of the completion of these DNS changes, the SpamStopsHere service will be in place.