Touhou music is (functionally) a genre of music that is based around artists/musicians arranging the songs from the Touhou Project, a solo indie bullet hell shooter game series, originally created in the early 2000s and became popular starting around 2007, created by a single person who goes by “ZUN”.
The key thing about Touhou music in general is that it is created by fans under a very loose and generous copyright rule set by ZUN — essentially, as long as you’re not using his assets and not commercially making money (selling at conventions or in small scale is OK), you can use the characters and music relatively freely.

Because of this, there is a literal unscalable mountain of Touhou music arranges from groups as small as a single person to symphonic orchestras; if you’ve heard it, there’s probably an arrange out there that mashes it with a relevant song from the game. It’s that sort of thing.

To me, the big sell of the Touhou Project is it’s premise; the plot revolves around a shrine maiden named Reimu who protects the border between the real world and a pocket universe where folklore creatures have retreated to now that they cannot sustain their existence in the real world due to lack of belief. Thus, the whole franchise has its canon based around belief, and when 99% of the cast are folklore monsters (many of which I have never heard of) who themselves represent concepts, ideas, and beliefs, there is a lot to unpack, and many of the songs have lyrics that I consider to be in a class of lyric writing of their own. You’re just as likely to find a troll song or a meme song as you are to find a song in the wild that talks about the nature of human existence, and that dichotomy is very appealing to me.

For now, I want to organize this by game.
There are 20 Touhou games; the first 5 are non-canon (and not on PC but an old system called PC-98) — the “newer” ones (starting with Embodiment of Scarlet Devil) have their own canon and rules.

My personal favorite game is Wily Beast and Weakest Creature, because the themes it covers on human nature and the human condition with an AI-themed final boss is just top tier. If you’re interested in playing the games, I would recommend Perfect Cherry Blossom or Imperishable Night first, though, the gameplay in those games is incredible.

Lotus Land Story:
Star Velocity – Felt

Embodiment of Scarlet Devil:
Lunar 11.3 Candle Light Magic – Shibayan Records
Alegria of Blasphemous Choices – Frost Fragment
Hiding You in the Night Sakura – Yuuhei Satellite
Clockup Flowers – Shibayan Records

Perfect Cherry Blossom:
Amazing 0 – Halozy

Phantasmagoria of Flower View:
Kachou Fuugetsu – Yuuhei Satellite

Mountain of Faith:
Hide and Seek of an Observing Crow – Shibayan Records

Scarlet Weather Rhapsody:
Kafka Naru Gunjou He – Yuuhei Satellite

Undefined Fantastic Object:
Twinkle Twinkle – Amateras Records
What’s the White Magic – A-One

Ten Desires:
Sweet End – Esquaria

Wily Beast and Weakest Creature:
Hanipaganda Album – Akatsuki Records
Idolatrize World – A-One

Unfinished Dream of All Living Ghost:
Chupacable Album — Akatsuki Records
Soliloguy of a Two-Faced Advocate – Yuuhei Satellite