Is it possible to receive and post replies to questions via e-mail; in a similar fashion to Google Groups and Facebook wall comments?
I guess you could combine the RSS feed available for every question with a RSS-to-Mail service like this one (I don't know it and whether it's any good, it just popped up first after quick googling) to achieve the desired result.
Stack Overflow themselves don't offer updates via E-Mail except for the "update me daily" feature and bounty expiry warnings, and it is unlikely that they ever will.
A Stack Exchange tag set can be configured to send you new questions via email, but there is no way to respond to questions via email.
To set it up:
Remember that Tag Sets work across all Stack Exchange websites, or you can use it on a single site.
I think there are dangers in providing an easy route to avoid logging in.
Having a large base of users who regularly log in is why SE is such a great place to go to get information.
There's no way that email is an appropriate way to send you all the world of things SE would like to offer you as opportunities for your contribution, (eg no one wants the review queue, the homepage or even a tag's contents in their inbox) so any way of interacting with the site discourages you from participating compared to logging in.
I think the site has seceral features designed to keep you logging in, this would seriously undermine them.
Making me log in when all I wanted was this feature was what changed me from a one-time visitor to an active contributor.