Funny how often people answer this very question by naming a song with a tune known as County Derry Aire--except it is not the tune notated a very long time ago as the County Derry Aire--which came across the pond & with lyrics added which was published in the States as "Danny Boy." Then, they often cite a jig--wasn't it from an English Street Opera ?--called Irish Washerwoman. And, they are likely to name several Tin Pan Alley songs written in the USA. Oh well, I love so many tunes & songs, I don't know how I could narrow it down to ten.