It has always been understood that moderators can and should email users that are abusive or have an issue that's best resolved privately offline. However, there have been a few suggestions recently that suggest that a broader approach should be taken.
First, in this discussion, it is suggested that moderators email users to follow up on the moderator flags that they leave on the site. My opinion is that this feature should be incorporated into the site, and that it's a bit forward to email another user, unsolicited, from my personal email address.*
However, it's this answer that prompted me to write this question. I think it's highly unprofessional, as a moderator, to email a user on behalf of another user, especially for something as trivial as a bounty. To me, this is clearly past the line. But the question is: where exactly is the line? When a user enters their email address (presumably to provide a Gravatar for their account) what communication does the user agree to receive?
* I might feel differently about this if I had a @stackoverflow.com email, and maybe some sample correspondences so that I don't feel like I'm starting with a blank slate every time I send an email