AOL offers IMAP access. Actually, with IMAP, AOL's a lot less dumb than it used to be--they offer large mailbox storage (not sure exactly what amount, but I have family members running on IMAP who have never run out of room) and fairly functional service.

However, I still prefer and second GadgetFreak's recommendation to look at switching to Google. So much functionality for free is just hard to pass up.