Molly Malone
Believe me, if all these endearing young charms
Bridgit O'Malley
Paddy on the railway
Down by the Salley Gardens
Star of the County Down
Goodbye to the thirty foot trailer
It's long, long way to Tipperary
Red is the rose that in yonder garden grows

No doubt some of these have American roots, and I'm sure that people will post and let us all know.