Library of Ashurbanipal, King of Assyria from 668 to 627, included personal letters written in cuneiform on clay tablets.
The telegraph and telephone come next in line; even if, as a recent NY Times article noted, the phone is experiencing a slow decline, it remains our oldest electronic social media. I'm old enough to remember the old "Reach out and touch someone" adverts for Ma Bell, and for a while, there was nothing more direct and personal than a phone call. Electronic mail protocols over ARPANET and its successors debuted in 1969, but did not become a common form of communication until the late 1980's; well before then, home computer users setting up BBS sites where they could post notices and download simple programs. My home town of Cleveland had a huge site, Freenet, where you could also get medical advice from doctors at Case Western Reserve and University Hospitals. The WELL, a large social site based in San Francisco, was the first home of integrated mail, chatroom, and file services; perhaps not coincidentally, it was also the site of the first case of online impersonation that went to court (a man was sued by two women for pretending to be a different, older woman who was a mutual friend).
In academia, the LISTSERV protocol brought people together by field and interest, and made it possible to, in effect, send a message to hundreds of people at once in search of advice or response; LISTSERVs were often associated with archives where you could search through older messages. Early online game spaces, such as MUDs and MOOs go back to the late 1970's, and many became highly social, with tens of thousands of "inhabitants" maintaining spaces there. All of these interactions were exclusively text-based, and the only "graphics" consisted of what could be cobbled together out of ASCII characters.
It wasn't until the arrival of the commercial internet in 1993, and the WWW protocol the next year, that social media really took off; by the end of the decade, Six Degrees, LiveJournal, Blogger, and eOpinion had launched. In 2003, Second Life offered its users a virtual retake on their first lives, albeit with a graphical interface that looks primitive by today's standards; that same year, MySpace became the first modern social networking platform, and a model for Facebook two years later. With half a billion users, including everyone from the President to the Pope to Batman (Adam West), it's well on its way to gaining the kind of cross-sectional critical mass to change the face of human communication.