We have most recently used Jangomail.com. They are small, but very, very responsive and helpful, extremely sophisticated (you can directly interface with your MySQL database and it will pull the addresses live at the time of the mailing, as well as update the list with bounces, remove requests, etc... as well as keeping a master list on their own servers.) They also offer free detailed spam analysis of your mailing (as to whether it will be identified as spam) and they will show you a rendering of your email in Google and Yahoo and a couple other popular web mailers, so you can make sure there aren't any weird rendering problems. And their deliverability seems to be excellent. I highly recommend them. They're also less expensive than Campaigner.

We tried using Campaigner for a couple months, but they were total nazis about the spam rate, even when we explained we were running one-time cleanings of old opt-in lists we hadn't mailed to in a while, and, quite frankly, we had a ton of billing problems and found their staff to be really arrogant.

But... you may also want to look at phplist, which is a free, open source mailer application. It handles bounces and unsubscribes (as well as subscribes) automatically, has very flexible list handling, sorting, and editing, and supports multiple lists and ability to mail to any or all lists, etc. Just make sure your ISP is aware of what you're doing so you have a good rapport with them in case you get a bunch of dumbassed AOL users marking the messages as spam.