There are a number of reasons why a composer or musician or band might want to release their music in some free form, say under an Attribution-ShareAlike license like CC BY-SA 4.0. (Wikipedia's Creative Commons license article gives a nice rundown on this important kind of licensing that permits free distribution of musical and other works.)
Famously, Nine Inch Nails released the album The Slip under CC BY-NC-SA 3.0 US, which encourages non-commercial enjoying, sharing, and adapting, provided that credit is given and any adaptations are licensed under the same terms. Based on the linked article, it appears the band still found ways to benefit financially in releasing the album for free.
Which is cool, right? Kind of like open source software. Kind of. I like to buy my music, because I don't have a great deal of ability to otherwise contribute to music creators. With open source software, there are tons of ways I can give back: testing, bug finding, bug fixing, documenting, writing my own stuff and contributing it… Given that perspective, I guess "free music" has never been all that interesting to me.
Nevertheless, there is a LOT of free music out there, given a flexible definition of the word "free." And some free music sites maintain historical archives of performances that would otherwise be lost due to lack of commercial interest.
Besides that, 2019 is a landmark year in free culture. An article in Hyperallergic explains that the United States' 1998 Copyright Term Extension Act, which extended copyright from 75 to 95 years, has essentially run its course. Therefore, works whose copyright expired will begin to enter the public domain again (in the USA).
With all that in mind, let's take a look at a few places where you can find free music.
Websites offering free music
The starting point for any search for free music has to be the Internet Archive's Audio Archive. You'll find "recordings ranging from alternative news programming, to Grateful Dead concerts, to Old Time Radio." Of particular interest is the Netlabels collection, with "complete, freely downloadable/streamable, often Creative Commons-licensed" works of all kinds. Right now I'm listening to "You Make You Feel (Diva Remix)" from Dumbo Gets Mad by Elephants at the Door. Awesome! And who doesn't love those old Grateful Dead concerts?
Another key free music resource is the Free Music Archive. After going through some challenging times recently, FMA seems to be re-established in solid form as of early 2019. As well as having a huge amount of interesting, clearly licensed music, FMA offers a great reading list, including links to other free music sites. I find myself often in the Old-Time/Historic section… Highly recommended.
Bandcamp, one of my go-to sites for purchasing music downloads, also offers music licensed under Creative Commons terms. Lots of cool stuff to check out here!
Music in Africa offers a considerable amount of music licensed under Creative Commons, along with articles on African performers, instruments, and musical styles. A great resource.
ccMixter is "a community music remixing site featuring remixes and samples licensed under Creative Commons licenses," although the site says "some songs might have certain restrictions, depending on their specific licenses. Each submission is marked clearly with the license that applies to it." Lots of interesting remixes (and re-remixes, and re-re-remixes…) here! Also some remixers explain how they did it. A very interesting site.
Jamendo is an important site in the "free enjoyment of music" end of things—it offers free streaming and downloading. The Jamendo Licenses page clarifies its meaning of "free"—to "allow individuals to stream and download [works] for free, in a non-commercial context, for personal enjoyment." While this is a limited kind of freedom, it has the merit of letting us discover new musicians that we otherwise might never encounter. I like that.
Although it's been around since 2004, I've only recently stumbled on the French "musique libre" site Dogmazic. Dogmazic claims to host "more than 55,000 musical titles, all freely downloadable 'in all peace and all legality.'" Dogmazic is supported, both by contributions in kind and by donation, from musicians and listeners under the auspices of Musique-Libre.org.
Ektoplazm is another longstanding free music site; according to its About page, it's been around since 2001. This site specializes in psytrance music and offers a nice historical perspective on both free music in general and psytrance in particular. I was especially interested in the comment that "as sales figures dwindled, labels were becoming increasingly risk-averse. Unconventional artists and newcomers were having a tough time getting their music released." Highly recommended, especially for its commitment to libre culture—freedom of enjoyment of content for fans, freedom of exposure for artists.
Some artists offer their work directly under Creative Commons licensing: Josh Woodward, Dexter Britain, Scott Buckley, Jason Shaw, and Matti Paalen pop to the top in a search for "Creative Commons music."
Websites promoting free music
The Creative Commons wiki is an important source of information about works (music and others) licensed under Creative Commons licenses. I find the list of online resources on its Musician page to be exceptionally informative.
Another interesting site is the Aula CM blog (in Spanish), which informally describes the various meanings of "free" and offers some useful links to free music sites.
Sound on Sound offers some ideas to musicians looking into Creative Commons licensing.
Musopen provides "recordings, sheet music, and textbooks to the public for free, without copyright restrictions." I like this site's organization—for instance, you can browse its music catalog by composer, performer, instrument, period, or form. If I select composer Tomaso Albinoni, it gives me his top 10 list and allows me to browse by music form (in Albinoni's case, concerto or sonata), instruments (chamber group, string instrument, etc), or period (baroque). Musopen also provides sheet music and sample performances for download. A really interesting and thoughtfully designed site!
Patreon seeks to establish relationships between creators and fans, both for the commercial benefit of the creators and the enjoyment of the fans. Some creators on Patreon offer their works under Creative Commons licenses; for example, Kathryn Rose says she feels "called to make [her] works available for all kinds of community and liturgical use. In turn, I'm community supported, not commercially supported."
And finally, if this isn't enough for you, check out Hongkiat's list of 60 Websites to Download Creative Commons Music for Free.
My list barely scratches the surface of Planet Free Music. As always, your search engine is your friend. Please be aware that lots of sites offer "free music" without carefully defining what "free" means, so be careful—always try to find a license, ideally a Creative Commons license as opposed to some complicated home-grown thing. Make sure you understand whether or not the license actually permits the kind of use you intend. And please think about how you're going to give back!