Like Russ, my sources are mostly forgotten, but not the songs. To add to his list (and I do these, too, all the time)

Hard Luck is the Fortune
Mary Hamilton
May Carol
Same Old Man (Sittin' in a mill)
I Gave My Love an Apple (and a later version, w/cherry)
Lots of chantys
Some old bluegrassy stuff
Lord Gregory
Johnny I Hardly Knew Ya
Shule Roon
and lots more