There is actually an entire industry for this, sometimes called the Email Service Provider (ESP) industry; it is also sometimes called Email Marketing.
If you search for "email marketing provider" you will see many of the big names in the segment.
For example, Lyris, Silverpop, ExactTarget, ConstantContact, MailChimp...
There are also different scales, some players will allow you to handle large volumes (e.g. campaigns of 100K messages at a time) and others that target small businesses (like MailChimp), where they are easy to get up and running quickly.
I believe if you spend some time on the websites of the providers above, you will learn something about the features available in the space.
We use one of the larger providers to send about .75MM messages annually. I also know that MailChimp has a free service for limited volumes to get started.
Good Luck, and let us know what you find and how you like it.