LibriVox has free public domain audiobooks.
Public domain works in the US are:
Anything published (in the US) from 1927 or earlier (this number goes up every year for quite a while), and
Anything published between 1928 and 1963 that wasn't renewed, and
Anything published before 1989 without a proper copyright notice.
(Don't go looking for things in that third category unless you've studied a LOT about copyright law. Mostly that covers things like "weird little newsletters" and "self-published booklets" and sometimes fanzines. But most publications have a copyright notice in them.)
There's also some oddball exemptions here and there; copyright law is a tentacled mess. But those are the basic guidelines. (Except for audio. Audio has its own set of rules. It's weird.) (I mentioned tentacles, did I not? Double the amount of them you were thinking of.)
There are a lot of works from the 50s and early 60s that were not renewed, especially short stories published in magazines.
Project Gutenberg began in 1971; the first text was the US Declaration of Independence, shared through the university computer system. That was the start of "hey computers + public domain text = FREE BOOKS FOR EVERYONE."