It looks like, after a bit of research, that there are a few big games in town when it comes to IMAP servers. The two main players are the UW IMAP server and the Cyrus IMAP server. Others include Dovecot, and Courier. There are more in addition to these, but these are the ones I've been looking at. You can find more at IMAP.ORG.
I've been reading a great summary by Mike Richardson on the different IMAP servers in the market, as well as an evaluation of the Cyrus IMAP server by Dianna Laakso.
It looks like if we move from our UW IMAP setup to the Cyrus system, we can get away from having a Unix user account for every email user, as well as using LDAP as our centralized user system. This will allow the user accounts that exist for email accounts, to be the same as those that exist on the main site, in the addressbook, etc.
At this point I'm worried about the process of migrating from UW to Cyrus since I can't find any single package that will just do it. It's not like we have a lot of users, but I'd still like to make it as easy as possible. Anyone out there have any experience with this? There is a single tool, mbox2cyrus, that I know of that will convert a users mailbox from mbox to Cyrus format. I'm not very excited about it though.