There are three companies that really stood out when I did my research. They are Oaknet Publishing, Revnet and Lyris. These lists are very different from those that allow posting to the list by list members. They allow up to 10,000 pieces mailed as often as once a week. I assume that after that, the price would increase.
Many people recommend Oaknet and are happy with their services.
Oaknet does have an affiliate program. Revnet sells mailing list management software. They will also manage your list without your having to buy the software. Revnet is a high-end service with quite a few features. The popular I-Sales list is managed by Revnet.