One thing that I will be very happy if added in Stack Overflow is a Private Message system like in forums, because there's some things that you want to be in private with your internet friends.
Normally people who want to be contacted will give their email address (or a website link) on their profile to allow for people to contact them. This has been discussed before and I really doubt that it will ever get implemented. The idea of the sites is supposed to be for Q&A, not extended discussions and social networking.
In my experience with various web forums, this feature is most commonly used by newer users trying get help directly from experienced users — to make sure their question gets attention from the bigger names at the site.
So now turn this around for a moment; if you were one of the more experienced users
*cough* would you want anyone and everyone to be able to send you a message like that? Would such a feature be useful, or would those users be more likely to just get swamped with junk messages? If they don't get swamped, is this fair to users that don't message these people directly? If you are planning to use the feature to discuss stackoverflow with your existing "internet friends", don't you already have good communication channels available to you for them?
This feature has been requested before and declined on UserVoice: http://stackoverflow.uservoice.com/pages/1722-general/suggestions/99462-allow-private-messages
it's about the questions and answers, not social networking. But if you want to contact someone, check their profile -- they will provide an URL or email address there.
I agree with everyone else here in that you can use email for that.
However, there are times I'd like to tell somebody something which; a) adds zero value to the community, and/or b) might embarrass the other person.
In those cases, it might be nice if we could flag a comment as private.
To be honest, I still don't know if this is a good idea or not, but thought I'd throw it out to the community anyway.