When I reply to a post, I can choose to receive emails when someone replies.

In Codeplex, I can elect to receive an email notification whenever a new issue is posted.

I have searched but have not found a way in these forums to be notified whenever anyone posts in a forum. Under the user control panel, there is "Manage Subscriptions" which states that I have not subscribed to any forums - implying that it is possible - but it doesn't say how.

Does anyone have any idea if it's possible and how to do so? I keep thinking I've missed the obvious.

I don't think there's a way of doing this in phpBB - but there is an RSS feed which you might be able to plug into something else.

For example new topics are in this feed: feed.php?mode=topics

Looking around for suggestions, there doesn't seem to be an obvious "RSS to email" service anywhere, but I saw a suggestion that IFTTT might do it - they can certainly take in RSS feeds: https://ifttt.com/feed

Yeah, I think RSS to email programs (the popular ones at least) require that you self-host the program somewhere. I've never seen a hosted one, maybe there's one out there.