Finally got around to setting up email support in the forums, so now password resets work, and by default users get email for the following:
Replies in followed threads (and you automatically follow a thread you post). You can either unfollow it or disable this setting if this gets annoying.
New chat messages (there is a rudimentary chat up in the top right; doubt anyone uses this).
Mentions, e.g. @vaette-test gets an email about this post.
All these can be disabled if annoying, in the user settings (the ones shown below are the current defaults, so unless you have changed something manually this is what you have):
Or, if you prefer, you can of course just enter an invalid email address and have the things rush off into the void.