Hi Tracy,
I use and recommend Aweber:
http://sswt.aweber.com - and for good reason. They are the industry leader in mailing list management and have the highest delivery rate available. They do allow you to host an unlimited number of mailing lists, autoresponders, and even blog broadcasts (automated email notification for blogs) in your one account for only $19.95/month.
You may consider starting out on a free or cheaper service to start, thinking you'll upgrade to Aweber later... but honestly you will lose most of your subscribers when you do that, so its best to just start out on Aweber (because trust me, every serious marketer ends up moving their lists there sooner or later
). For more about it, see my thread in the Email Marketing section here at the forum. Its a sticky thread at the top of the category titled "Choosing A Mailing List Manager" (I think I'm remembering that title correctly).