Right now I'm aware that there is no Private Messaging system and that almost (if not all) request for creating one have been denied. Most likely because of the difficult nature of such a system and the amount of data a Private Message system could take up. So I'm not suggesting a feature that creates a Private Message system. Instead I'm suggesting allowing the user to integrate his/her Facebook or other social network profile into Stack Exchange.
The hooks seem to be in place for using the Facebook ID, but I'd rather like someway to post a private message to his/her Facebook on Stack Overflow. This will allow you to have a PM system without creating one, and it would be 100% an opt-in feature. Not everyone likes the idea of sharing their profile information. I would also like to suggest that a certain amount of repetition be hit (say 100) before the user could activate this ability and a smaller amount (say 15/20) before a user can message someone. This is of course to weed out any junk messages.
I know that a fully extensive Stack Exchange API exists and if someone wanted to they could recreate the stack overflow sites with this feature, but its a small concern that seems to be growing in the community. I'd rather like this feature implemented, and I believe the feature could be implemented easily.
Another way to use this feature instead of Social Network connections could be an e-mail button right from the profile. Same repetition restrictions as before, but instead of showing the e-mail the user would enter the message an in form mailer and it would be the users choice to respond and share the message. (Change the Reply-To header field in the message to the actual users message.)
I've noticed that these features, and like ones, that would be nice and benefit the community have been declined. Therefore I implore you to wait a few weeks before making a decision to see if enough of the community wants this feature. It doesn't seem that difficult to me to add such a feature but I'm not a Stack Exchange developer and I really wouldn't know. Just please do me the kindness of giving a reason if this feature is declined.