Copyright law is complicated and becoming more so. But there are ways you can look up whether an old song is in the public domain.
Prior to 1978, copyright lasted for 28 years, but could be extended for an additional 28. As Disney lobbied desperately to keep their old Mickey Mouse shorts from ever becoming public domain (expect another extension in about 5 years!) more and more time has been added to the renewal period. At present, any old song or book is automatically in the public domain if it was published 95 years ago, so anything published prior to 1923 is in the public domain. (This does not include musical recordings, which have their own complicated copyright system.)
BUT--what if the copyright was never renewed?
My search started because I have a 1939 easy piano book with the songs from the old Fleischer cartoon, Gulliver's Travels, a movie which is actually in the public domain, and I wondered whether it was okay to scan and share the music.
After hunting on the web, I found this incredibly useful page with succinct copyright information and links to sites where you can search for old copyright information.
For items copyrighted after 1978, there is a convenient searchable database.
For older works, you can get links to the copyright catalogs on this page:
First I checked the 1939 listing, which opened in Google Books and was searchable by keyword. I searched for Rainger (one of the composers) in both volumes, and found that the Gulliver's Travels songs were indeed registered in 1939. Bluebirds in the Moonlight was listed in two versions, one from Gulliver's Travels, and one from Man About Town.
Renewals have to occur during the 28th year of copyright, so you need to check 27 years after the original registration.
The 1966 link was not searchable, but provided a scanned PDF of the Copyright Office catalog. The Man About Town version of Bluebirds in the Moonlight was listed as renewed. None of the Gulliver's Travels songs were listed.
So, it seems that the songs from Gulliver's Travels are in the public domain! (With the possible questionability of Bluebirds in the Moonlight.)
Hope this helps some of you find free music!