According to this Lexis/Nexis story, it's happening around the world, but not (yet) in the U.S. In the U.K., even Twitter has been used:
In September 2009, the High Court allowed an injunction against an anonymous blogger to be served via Twitter. British lawyer and conservative blogger Donal Blaney obtained the injunction after an unknown blogger began impersonating him on the Internet.
Dan Canton at Slaw says that Canada is getting into the action:
We have seen a few published cases where a court will order the service of a document by way of a defendant's social media account.
I had the occasion today to talk to a couple of lawyers who do collection work. Anecdotally at least, the actual practice seems to vary by province and location. That is not surprising considering how new the concept is, how traditionally lawyers and judges tend to think, and how rules of practice differ.
A lawyer from Alberta mentioned how they routinely obtain orders to serve documents by facebook. He commented that it is acknowledged that this kind of service against a person who can't be found or evades service is in practice much more effective than the traditional method of advertising in a newspaper. And far cheaper as well.
The same lawyer mentioned how they often service documents via email. His office will phone a defendant, and ask if they can serve the claim by email, explaining that service by email will result in smaller costs being assessed as part of the judgement. They then have the court approve the service after the fact based on an affidavit of the person who made the call and sent it by email. It can cost less for them to do that than to pay a process server.