One of the projects I've worked on recently is the ability to reply to forum posts by e-mail, and I'm happy to announce that a prototype of the functionality is now available. This request was originally raised in MDL-3714.
I'm still working on documentation, and some of the language strings will need adjusting, but the prototype is otherwise fully functional.
To access the prototype site, you will need to create your own account at http://prototype.moodle.net/verp, where instructions on how to use the prototype system are provided, along with some suggestions on other things to try.
The system I've conceived allows for much more than just e-mail to forum replies. There is an extensive API which be used to create a message handler for almost anything within Moodle. As an example, the above prototype site also includes an e-mail to private files feature. The full details can be found in the parent issue, MDL-47194.
The initial developer documentation is available at https://docs.moodle.org/dev/VERP, with API documentation available available at http://prototype.moodle.net/verp/apidocs/classes/core.verp.handler.html.
There is one caveat that I have discovered - when using Google Mail, and replying to an e-mail whose Sender is an address that is one of your verified e-mail aliases, Google ignores the "Reply-To" header. I'm trying to find a solution for this issue, but without success so far.