The legal uses of copyrighted material in the U.S. are explained in American University’s excellent Best Practices in Fair Use brochure.
Fair use covers only a limit set of uses for copyrighted works,but public domain material can be used for any purpose. To see what works have passed into the public domain, try a summary of the rules in table or flowchart form.
As I understand it, here are the basic rules on what’s in the public domain:
1. All works published up to and including 1922 are free to use. Research challenge: basic (just confirm the publication date).
2. Some works published from 1923 up to and including 1963 are free to use. I would say this is always worth checking. Research challenge: intermediate (using publicly-available online sources).
3. Very few works published from 1964 up to and including February 1989 are free to use. It may be worth contacting the publisher or paying for a search at the Library of Congress (see below), but don’t expect success. Research challenge: advanced (this will likely involve phone calls and a research fee).
4. No works published from March 1989 onward are ever safe to use without permission from the rights holder. Research challenge: advanced to impossible (the rights holder might charge an expensive license fee, deny you permission, or just refuse to speak to you; an unscrupulous rights holder might also lie about what rights they actually own).
In all cases, when you run into obstacles, remember to check whether your use of copyrighted material might conceivably be covered by fair use rules. While the U.S. has some of the world’s strictest copyright laws, it also has the world’s strongest fair use protections.
Unfortunately, even in cases where you’re technically in the right, distributors, broadcasters, ISPs, and content aggregators will often become frightened of legal trouble and refuse to touch your work. The Electronic Frontier Foundation provides legal advice for artists and defends people unfairly accused of copyright violation.
More resources:
Here’s a searchable U.S. copyright renewal database to confirm the availability of works published between 1923 and 1963. If your work does not turn up in the search, that’s good–it means you’re probably OK. The records can be downloaded as an XML file too.
If your use of the work is going to end up on broadcast TV or something similar, you may need to buy extra protection by forking over US$150 to the Library of Congress for a letter of confirmation. (No refunds, so be sure to use these tools and confirm it yourself first!)