If you go to your local library and look up "folk music" books or CDs, you'll find a motley collection, including compilations by the late Tom Glazer and other collectors.   As to what songs are commonly known and sung, that does vary widely depending on location, ethnicity, etc.   Here are a few songs I find just about everyone knows (can sing along with) in just about any song circle or sing-along I find on the west coast of the US:
Will The Circle Be Unbroken
The Last Thing On My Mind (Tom Paxton)
Swing Low, Sweet Chariot
Me & Bobby McGee (Kris Kristofferson)
Amazing Grace
Red River Valley
The Wabash Cannonball
Tennessee Waltz (pop song from 1951)
Take Me Home, Country Roads (sung by John Denver)
Leaving On A Jet Plane (as recorded by PP&M)
Blowing In The Wind (Bob Dylan)
Danny Boy
Tom Dooley
Sloop John B
You Are My Sunshine
Over The Rainbow (from The Wizard Of Oz)
Hard Times Come Again No More
Edelweiss (from Sound Of Music)
(Of course on some of these songs, it's just the chorus that everyone knows.)

In Jewish-American communities everybody knows Hava Nagila and Tumbalalaika (the chorus anyway) and Havenu Shalom Aleichem, for example, as well as Sunrise, Sunset (from Fiddler On The Roof).   Mexican-American groups will know Cielito Lindo, De Colores, La Bamba, etc. (I lead sing-alongs in a variety of settings and it's not unusual for a group to be heavily represented by people of one ethnic heritage or another.)

Songs "everybody" knows in the US but few people ever sing outside of children's or senior citizens' (e.g., nursing home) groups include:
Take Me Out To The Ball Game
Shine On, Harvest Moon
My Bonnie Lies Over The Ocean
I've Been Workin' On The Railroad
Down In The Valley
My Darlin' Clementine
O Susanna!

I realize that many of the songs I've listed aren't "folk songs" as most people define that term, but in a way, once a song becomes so commonly known that pretty much a whole population, spanning more than one generation, spontaneously sings along with it and knows it by heart, you could say it's become a "folk song" even if its author is known and it's not PD.