Redmine has turned out to be a great Project Management tool for us. It is free and has an active development community. Turning this email feature on was very easy. I followed the instructions here. I chose the IMAP optionas it seemed the easiest route and works great.
Using the IMAP method, Redmine checks an IMAP account for email responses to issues at an interval you set. When it finds responses that match issues, it imports them and applies their changes to their respective issues. In addition to adding the reply as a comment to the issue, other things can be done, such as assigning the issue to another user or closing the issue. This is done by using keywords in the email body. More is explained here.