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.
The licensing descriptions do not constitute legal advice. I am not your lawyer. Please verify with the website, as the license descriptions may be inaccurate, or the licensing terms may have changed.
ASOBEAT - the Google Sheets contain free download links; credit required unless you purchase the lossless Bandcamp versions
Ontama - 500+ songs; OGG/MP3 versions are available; credit not required.
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.) Offers convenient (and free!) bulk downloads.
Warning: The rules seem a little contrived. Most notably, there is an expectation of not distributing the verbatim music files for commercial works, potentially including as asset files - this may rule out usage in f.e. video games unless some kind of DRM scheme is implemented.
SLOS -
English licensing terms (credit required, notification required, providing a copy of a finished commercial work required); premium licensing exists but not outside of Japan
TAM Music Factory - around since 1998! MP3/OGG/MIDI versions are avaialble. Credit not required for non-commercial use, required for commercial use; no need to notify TAM since June 2021; some songs can have the credit requirement waived for a fee. Some types of content (18+, sensitive, etc.) are not allowed - check with the website.
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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.
MusMus - credit required for royalty-free use, license can be acquired
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