You can use FogBugz to handle customer interactions over email. If you're using FogBugz On Demand, your FogBugz comes with a free cases@xxx.fogbugz.com mailbox to get you started. If you have FogBugz on your server (or if you want to use an email address of your own with FogBugz On Demand), you'll just need to have a POP3 or IMAP mailbox hosted on a server that FogBugz can access.
Once you've set up your mailbox, FogBugz will check it regularly for new messages. When it finds messages in the mailbox, it'll download them (including attachments) and turn them into cases. Once the email is successfully turned into a case, it's deleted from your POP3 mailbox or marked as read and optionally deleted if the mailbox is IMAP.
By default, FogBugz will send a confirmation email automatically. This email will contain a link to a special public view of the case page.
By default, once a case is created in FogBugz, it's autosorted using FogBugz's sorter. This is not just a spam filter. It's a probabilistic sorting engine that can learn how to sort different kinds of emails into different areas within the Inbox project. It can save a lot of work if you have different teams working in the Inbox.
Once the message is in FogBugz, you can treat it like any other case: you can prioritize it, assign it, track it, slice it, dice it, deep fry it, etc. But probably you'll just want to reply to it. Your reply will come from the same email address the original message was sent to. If the customer replies, the email will reactivate the case if it's been resolved, and will re-open it if closed. To ensure timely replies to customer email, you can set the mailbox to assign a due date to the case that was created.
For several reasons, it's probably a good thing to keep all your incoming customer email case in your Inbox project. (FogBugz can be configured to sort into projects other than the Inbox on a per-mailbox basis.) If a given case seems like it should be turned straight into a bug, we get the best results with spawning off a new case, and using FogBugz's automatic case relation feature to link back to the generating email. We do this for two reasons: First, the FogBugz autosorter uses historical data to decide where to sort an incoming email. If your email cases are moved out of the Inbox project, the sorter loses track of them and becomes less effective. Second, and more important, we find that Inquiries demand a different kind of attention than Bugs or Features. If you move a case out of the Inbox and into your feature backlog, it's just too easy to forget that you didn't respond to the customer... and customers like getting responses to every email. When the feature is implemented or the bug is fixed, you still have the case relation link back to the original email, so with two clicks you can reply to the customer to let them know.
When you do respond to the email, FogBugz has a lot of help for making it painless. You can use our keyboard shortcuts to burn through a list of cases quickly. You can use snippets to create friendly salutations and closings, as well as clear responses to frequently asked questions. FogBugz also helps prevent users from stepping on eachother's toes when responding to emails and relates any other cases with the same correspondent so you can quickly see the customer's history.
Customers can also submit new cases via public projects, and can post on public discussion groups (you can turn a discussion post into an internal case with one click).
For guidance on setting up your mailbox, see this article.