Yea, this is one of the main reasons I use FogBugz. It checks email via POP and then imports emails as cases. You can handle the case just like another case/ticket/bug. You can reply right from the website, or assign it to a project, user, etc...
They have a free startup plan for two users, and free unlimited users for yc funded startups.
FogBugz rocks. I've been using it for almost three years - the last year using the Fog Creek hosted version - and I couldn't be happier.
As mentioned, you can give it POP access to your support account and it will auto-respond to your customers (optionally) and also create a new "case" for you to track the issue. It makes it dead simple to follow a thread all the way through until it's resolved.
You can also see the history of previous cases opened by the same person which can be very helpful. FogBugz also includes a wiki to help share information internally, the same forum software that runs the BoS forums over on Joel's site, and some pretty cool project mgmt features that I personally don't use, but could see the value in if I had a bigger team.
I know not everyone drinks the Joel Kool-aid, but FogBugz is pretty slick. I'd say it's worth checking out, especially if you quality for their free plan for students/startups. http://www.fogcreek.com/FogBugz/StudentAndStartup.html