I understand, from visiting the Public Domain site, that almost everything written in the US after about 1924 is still under copyright. Even with old folk songs, you have to be careful, because certain versions (specific verses, arrangements, are under copyright).
E.g. Irving Berlin owned the copyrights on most of his songs, because he published most himself. "Alexander' s Ragtime Band," however, which he wrote in 1910, is in public domain.
George Gershwin published many songs in the late 1920's and he died over 50 years ago, so one might expect that some of his songs would be in PD. But I understand his family (no children) has sued (successfully, it would seem) to extend the copyrights.
Personally, I would love more information about this.
His brother Ira did not die until the 1990's I think, and Ira was lyricist on many of George's songs.

Even "Happy Birthday," should still be under copyright, since its author died within the last 10 to 15 years, and the current copyright law, if I am not mistaken, is "author's life plus 50 years."