Do you really not backup your mails? Do you consider them not important or do you glorify your provider? I highly recommend making your own backups for anything you consider worth saving.
It's the practical realization that Google is likely to have a more recent, redundant backup of my data than me. The amount of effort to ensure that P(losing my backup) < P(google losing a backup) isn't worth the effort except for a few very important pieces of data.
1) Offline copies: Either because I have no internet access or the webmail provider is down. For my company e-mail "Google is down" or "I can't get online" is just not a good enough excuse when such an easy solution exists. Even if you primarily use webmail I would highly suggest mirroring a local copy via IMAP if you're dealing with important stuff.
2) I like being able to segregate my mail into its own space. I maximize my mail client full screen and have other windows on my second display such as individual messages or notes, address book, calendar, etc. I find this to be more appealing than opening half a dozen browser windows and clicking through different sections of GMail.
3) Nothing beats the performance of a local store. My IMAP server keeps a full backup so any one client losing its local copy isn't a problem. Searches are instant in Apple Mail, I can bounce between different folders/messages with no penalty waiting for another GMail page to load.
4) No distractions. When I have to sit down and pound through lots of e-mail being in a browser makes me less productive.
Have all your mail in one central place without being tied to a single box with a particular config. You can even use desktop clients on multiple computers via IMAP without any hassles.
Then search in ALL of them is INSTANTANEOUS!
I wasn't using Gmail due to the non-functional search for word fraction. And my IMAP server's search took almost a minute sometimes (dovecot + extra indexing options). But this is... unbelievable.
I tried Gmail and other mail clients, but I've been in Thunderbird since 2007 now.
I love the speed. I use it for work email. I like the tagging. I like the speed. I click and email opens. It doesn't matter how slow my connection is right now. It's easy to backup to an external hard drive. When my browser crashes, my email does not. I like how the folders work. The spam filter is awesome.
Buy mostly, it just feels like home to me. I don't know how to explain it, but I love being in Thunderbird, and I just can't operate without it now.