Whether or not a song still has a valid copyright depends on a number of factors, not the least of which is when it was first published. Generally, copyright is now life of the author plus 70 years (special rules apply if the "author" is a company). The Copyright Act has changed several times since 1900 and each variation applied different life, and all key off of when the song was first published.
Works published before 1978 have a life of 28 years but can be renewed once. Generally, however, copyrights cannot be renewed.
A work enters the public domain after its copyright expires. The work may now be used by anyone without consent of the author. As was mentioned, a new arrangement of a public domain song may be copyrighted (that is, the arrangement is protected, not the underlying work). For example, in the 70's when there was a rash of "disco-ized" classical tunes (A Fifth of Beethoven comes to mind), the arrangements were copyright protected even though the underlying composition (Beethoven's fifth symphony) has been in the public domain for ages.
Contrary to popular belief, there is no "magic" amount of a copyrighted song that can be copied or "sampled" without liability.
Go here for some good info: http://www.copyright.gov/help/faq/