This is not meant to be an exhaustive list; rather, it's a personal list of artists and websites which caught my eye and which I might find myself going back to in the future.

Entries in bold are personal favourites.

Remember, if you want music fine-tuned for your project, you're going to have to pay for it.

• DOVA SYNDROME - popular royalty-free music repository in Japan, with many contributing artists; make sure to check the license for each file you download; if you're in Europe, using the YouTube channel may be an easier way to browse through their work.
• OpenGameArt - mixed bag quality-wise, some real hidden gems exist though; has a strong focus on using CC-style licenses.

• Alcaknight - 100+ songs, piano-centric, with a visual novel vibe; must be downloaded from SoundCloud; CC-BY 3.0
• ISAo/AIRYLUVS - OGA-BY 3.0; more songs by the same artist available under other licenses
• OtoLogic - CC-BY 4.0
• Steven O'Brien - CC-BY 3.0; note that not all of the artist's music is Creative Commons

• Peritune - 300+ songs; OGG/M4A versions are available for free for royalty-free use, lossless WAV versions must be purchased; credit appreciated but optional; premium BGMs available. (While the “about” page lists CC-BY 4.0 as the license, the other terms are contradictory.)
• Kevin MacLeod - if you've ever been to the Western Internet, you've heard his work. Has music for just about every occasion. Nobody got fired for using Kevin MacLeod BGMs.
• Ontama - 500+ songs; OGG/MP3 versions are available; credit not required.
• Wingless Seraph - mostly game-centric songs; credit required.

• Battle of the Bits - chiptune community with CC BY-NC-SA licensing. This is quite more restrictive than the typical expectation for “royalty-free music”, but if you're working on a jam game or a homebrew game, you might find this restriction irrelevant.

These contain more artists than my own, so…!

• LemmaSoft forums' royalty-free music list - made with Ren'Py users in mind