OK... I've not had a private conversation with anyone yet on Xenforo. Do you by default then get an email notification someone has messaged you?
If yes... then some members will want to turn this off.
If no... getting an email notification that someone has messaged me is pretty critical to me, since I don't want to have to log into my forum continually just to check for new messages, I thought this was a pretty standard feature on any forum/networking site. Taking it a step further, the email contains the new message text itself (so you can decide whether to log in and reply).