I really love original Touhou-style songs. I actually have more of these on my computer than arranges.
I suggest making a NicoNico account if you haven't got one yet. Some of the composers post their works there from time to time.
Anyway, here are some of my favorite songs, with links added for your convenience:
Older stuff:
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東方ファミマFirst original Touhou song that I ever listened to. Mind blown.
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4面以降のBOSSっぽい曲Used to listen this song back in 2010. Really like the intense beginning.
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風吹く地の暁星 - Dazzling StarQuite a simple song. The style reminds me of STB.
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旧作風 - Experiment!!Original PC-98-style song.
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雨の降る夜にSupposedly a theme for Daiyousei. Very dramatic.
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シンデレラサイレンス ~ Come Cute Chu.Beautiful until 1:20, pretty ugh after.
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なんとなく東方っぽいオリジナル曲を作ってみたたI'd really like to play a stage with this song as BGM...
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Newer stuff:
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宵宮の宝石箱Opening theme from Treasure Castle Labyrinth (not a game.)
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ディープ・アクアマリンStage 3 theme of Treasure Castle Labyrinth. The style reminds me of GFW.
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玉石の協奏曲Stage 5A theme of Treasure Castle Labyrinth. Most of the song is a buildup for a nice part with ZUNpets.
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水晶華灯怪導Extra stage theme from Treasure Castle Labyrinth. One of the most energetic Touhou songs I've ever heard.
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少女達の弾幕浪曼Last Word Theme from Treasure Castle Labyrinth.
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天涙流々 - Princess's wishOpening theme from Heavenly Gathering of Clouds (not a game).
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本日ハ雨天ナリStage 2 theme from Heavenly Gathering of Clouds. Love the bass.
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数奇な女神の采配Track 04 from 東方不調和. Reminds me of the Stage 3 theme from TD.
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秋風に吹かれてNicoNico goodness.
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三千八百億平米神話大系Theme of Watatsumi Ryouhi from Touhou Gishinreibyou.