Migrate IMAP email to Linode?

I'm thinking about migrating my email from a shared hosting service (one of those cpanel-based ones) to my own Linode, and the process of setting up the MTA/MDA doesn't look that daunting. What concerns me is that I don't want to lose years of messages in folders on my old service.

Is there a programmatic way to migrate all my mail on an IMAP server? I don't have a high volume of mail--mostly personal--but do have several users and would like to do it in as seamless a manner possible.