Oldest (and largest) genealogical society in the US: New England Historic Genealogical Society
They have an active home on FB (as a non-profit "person").
Second oldest: New York Genealogical and Biographical Society (informational page on FB as an "interest" copied over from the wikipedia entry)
I'm a big fan of the NYGBS, mostly because I find the online back issues of the Record to be stunningly useful. It is worth pointing out that NYGBS -- ancient and huge -- gave its library to the New York Public Library (including the manuscripts) back in 2008. Because they could see the move from showing up in person to use the library to preferring online access very, very clearly.
"The board of trustees analyzed the state of the NYG&B and studied the field of endeavor in which it operated. The board ultimately decided that the business model, in place for decades, had become unsustainable." They gave the library to the library. They partnered with NARA Manhattan and NYPL in developing "The New York Family History School" to meet their educational mission. They publish a magazine (which is actually worth reading). And they supply back issues of The Record digitally online along with other resources.
NEHGS has _not_ done a massive pivot a la NYGBS. I don't think I expect them to. New England isn't known for being early adopters. Will the next few years suggest that one decision was "right" and the other decision was "wrong"? Almost certainly not. Both societies will continue into the indefinite future, serving to help us search the misty reaches of the past. Size counts for a lot.
Googling on largest and biggest exposes an adjective problem: distinguishing what is a "state" society from what isn't a "state" society.
The Ohio Genealogical Society claims to be the largest state society. http://www.ogs.org/about/mission.php (Does that mean NYGBS isn't a state society? What _is_ a state society? I don't care enough, I suspect. But I may.)
That's sort of a weird mission, including details like:
"Securing and holding copyrights, master copies and plates of books, periodicals, tracts, and pamphlets of genealogical and historical interest to the people of Ohio. Publishing, printing, buying, selling and circulating literature regarding the purposes, records, acquisitions and discoveries of the Society."
It's also a long mission statement, which suggests that all those people who hate long mission statements might be on to something. OGS seems to have multiple lineage societies associated with it? They also have an active Wall on FB.
The Massachusetts Society of Genealogists is a "group" on FB. Entertaining mix of recent posts includes someone wishing (me too!) for genealogy software to arrive for the kFire -- and comments that participants in the indexing project can't be running 16 bit hardware. Yikes! But I'm sure necessary and valuable information.
I asked to join a few minutes ago and have already been added. The comments include _successful_ requests for experts to help on particular topics, so this group is functioning really well.
In response to some of the blogger/society debate, I went looking for ways to participate in indexing/transcription projects. Ancestry.com failed me (no Mac software, as near as I can tell), but FamilySearch worked and I spent about an hour trying it out. MSOG has a group working on a Boston-area project they are encouraging members to participate in. This seems like _exactly_ what a regional/local genealogical society should be doing to leverage national level technology in service of local/regional goals. Altho, ew, I used leverage as a verb. Sorry.
Oh, and I've now stumbled across a genealogy blog that is so unbelievably cool I'm going to take a break and go read back through it for a while.