Now, not everyone falls into the category of user which originally motivating the introduction of IMAP. That doesn't mean there aren't good reasons for you to use IMAP. Here's some reasons I've found to be greatful for IMAP.
A lot of peole have work and home e-mail mailboxes. They read each exclusively at one location and one machine. This means that sometime you don't get a message for a for several hours just because it arrived a few seconds too late (either just after you went to bed at night, just after you left work in the evening, or if you are like me, just after you left for work in the morning ;-). While in most cases it's not urgent, this can lead to cases where people send you e-mail to BOTH locations (indeed, I've actually encouraged people to do this in the past). IMAP can simplify this problem. Presuming your office firewall doesn't block it, you can read your home e-mail from both locations, and presuming it doesn't violate company policy, the reverse is also true. This also means that that all important document you forgot to print out before you left the office can still be retrieved from your e-mail once you get home.
If you're a programmer, you frequently find that you are developing on different platforms and therefore different machines from time to time. Rather than having a dedicated "mail reading" machine, why not just be able to read your e-mail from any machine?
If you're an executive or salesperson, you may have both a PC at your desk and a laptop for the road. Now you don't have to hook-up your laptop the LAN everytime you want to read mail.
For many people, loss of e-mail is a disaster with unimaginable consequences. Yet, they store their e-mail one of the most frail repositories available to them: their local machine. Not only is it likely not backed up to tape on a regular basis, it also is exposed to much harsher environmental conditions than your typical UPS protected, temperature controlled, low traffic area server. If you keep your mail on a laptop this is only exacerbated. On top of all this there's a good chance the machine will be replaced in a few years, and you'll somehow have to move all your e-mail onto the new machine. Why bother with this mess? Keep your mail on the server where it's relatively safe.
If you're a Linux user, there's a better than average chance you dual boot between Linux and Windows. That can be annoying, but what's more annoying is having to reboot to another operating system just to read your e-mail. IMAP solves this problem: now you can access your e-mail from both OS's, no problem!
Finally you can avoid having to wait while you download those huge messages sent to you by some SPAM company just to get to that all important message that will determine the future of your career! ;-) IMAP let's you decide which e-mail you want to download, and if you're ISP will let you filter your e-mail on the server, messages can be already sorted for you before you login!
So, you've finally given up on your old mail client and you're ready to go to a new one.... Great, now you just have to convert the 5,000 messages you've accumulated over to the new mail client's format... Wait? There's no conversion program? You're SOL! IMAP solves this problem, because your messages are all accessible through a standard protocol. So you can change e-mail client's each week if you like.