Hard Times Come Again No More (one of those songs everyone just seems to know)
Ain't Gonna Study War No More (aka "Down by the Riverside"), I Went Down to the Valley to Pray, (and other "zipper" songs)
A lot of people know John Denver songs (the choruses, anyway) without having consciously learned them: Country Roads, Annie's Song
Then there are the call & repeat songs like Sippin' Cider and The Other Day I Met a Bear
And songs with a refrain rather than (or in addition to) a chorus, like Gone, Gonna Rise Again, or Shut De Door, Keep Out De Devil
More Paxton: Ramblin' Boy, Home to Me is Anywhere You Are
Steve Goodman's City of New Orleans
If I Had a Hammer
Today (While the Blossoms Still Cling to the Vine)
Sweet Violets
Raindrops Keep Fallin' on My Head
Songs from Musicals (again, songs people don't necessarily know they know): Matchmaker, Hello Dolly, New York New York, Edelweiss, Lonely Goatherd; So Long, Farewell; Do-a Deer, Climb Every Mountain, I Feel Pretty, Maria, Tonight, There's a Place for Us, Clang Clang Clang Went the Trolley, Oklahoma, People will Say We're in Love, Oh What a Beautiful Mornin', I'm as Corny as Kansas in August, There is Nothing Like a Dame, Gonna Wash That Man Right Outa My Hair, 76 Trombones, I Love You a Bushel and a Peck, Luck Be a Lady Tonight, Only Doin' it for Some Doll, The Age of Aquarius, Hey Big Spender, When You Walk Through a Storm, etc...
WWI & WWII songs: Long Way to Tipperary, Pack Up Your Troubles, There'll be Blue Birds Over, Don't Sit Under the Apple Tree, Long Long Trail a Winding (here's a great WWI website to find (among other things) words to WWI songs that everyone knows the chorus to, but not many of the other words)
Also: Motown Songs, Beatles songs, Gospel songs, rounds, TV themes can be fun, too

Have fun!