Well, surprisingly, probably the easiest place to start using IMAP is at work. If you look at my short list of IMAP servers you'll notice that the most common messaging servers you'd find at work are all listed there. In all likelihood, all you need to do is change your configuration to use IMAP instead of whatever protocol you're currently using, and you're in business.
If for whatever reason, you don't have IMAP support, it's pretty easy to lobby for it. If you look through he benefits of IMAP, most of them would be of interest to a business. Businesses might also like the fact that all the mail is stored in one location.
Well, the logical next question is, "Which ISP's support IMAP?". The short answer... "none of the above". I don't entirely understand this. While IMAP certainly requires significantly more ISP resources than POP, I think this can easily be compensated for by charging people for additional disk space. IMAP servers also avoid the problem of e-mail getting "lost" when a POP client crashes after a download, but before it writes to disk. I strongly encourage everyone to ask their ISP about IMAP support, and if you're an ISP reading this, START SUPPORTING IMAP!!! In the meantime, you need to look elsewhere for solutions.
If you're as fortunate as I am, and you actually have a permanent Internet connection with a static IP, it's quite simple (and handy) to become your own mailserver. Just register the domain you want you're e-mail address to be at (in my case xman.org), and then configure your DNS so that there's an MX record for that domain which points to your system.
Now, of course, this doesn't include all the insanity of setting up mail on your system. I'll gloss over that because it depends a lot on which MTA and MDA you're using. The key part of the idea is to ALSO setup an IMAP server so you can access your mail. This approach works well, as your mail is always accessible over the Internet, and you can properly configure your authentication (SASL) so that logins to your mail server don't broadcast your password all over the Internet. :-(
What if you don't have a dedicated IP address or a dedicated connection? Fear not, all is not lost. Eric S. Raymond of Cathedral and the Bazaar fame has a solution for you: Fetchmail. Fetchmail is a weird play on the concept of an MAA. Fetchmail acts like a POP,IMAP or whatever client and downloads your messages.... and then delivers them to your local mail system as if that had always been their final destination!
How does this let you use IMAP? Well, you setup fetchmail to pull e-mail messages down from your ISP on a regular basis, and then you have the messages delivered to your local MTA. The messages will get delivered on your local machine so that you can access them from your local IMAP server!
Now, this approach is less than perfect. For starters, getting e-mail remotely may prove difficult, as you'll only be able to do this when your machine is connected to the Internet and you know it's IP address. However, you'll still have a lot of flexibility in terms of switching between mail clients. You'll also have access to all the power of IMAP. Of course, this also lets you apply server-side filtering rules. Of course, by having your own local MTA it's also easier to SPAM your ISP for requests to support IMAP. ;-)