I'll try to make a list of the songs you can find in the game
Note that the game uses MIDIs
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Main Menu / Sound Test Track 1: Tengu Man - Mega Man 8 (Sega Saturn) / "Ruined Area" - Intro Stage - Rockman 8: Metal Heroes / Maelgrim http://maelgrim.tripod.com/Rock8mus.html
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First cutscene / Sound Test Track 2: Panic Puppet Zone Act 1 - Sonic 3D Blast / Twinkle Cart - Sonic Adventure
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First cutscene / Level 5 cutscene / Sound Test Track 3: Round 3 - Forest Fortress - Area 88 / U.N. Squadron (Capcom)
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First cutscene / Sound Test Track 4: Unknown, could be from Final Fantasy, the music has similarities with Go Above the Clouds! - Final Fantasy III
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Level 1-1 / Sound Test Track 6: Super Mario Bros. 1 Overworld - Super Mario All-Stars
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Level 1-2 / Sound Test Track 7: The Kids Aren't Alright - The Offspring
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Level 1-2 (skateboarding) / Sound Test Track 8: Sector Alpha/Sector Beta/Rainbow Road - F-Zero X
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Level 1 End cutscene / Level 3 End cutscene: Super Mario Bros. 1 Overworld (Remix)
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Level 2-1 / Sound Test Track 5: ENEMY: CHAOS (or Boss: CHAOS ver. 6) - Sonic Adventure
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Level 2-2 / Level 4-2: Venus' Theme - Sailor Moon S (Game)
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Level 3-1: Hitohira, Kasumi's Theme - Dead or Alive 2
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Level 3-2: "untitled", MIDI by Paul Lapensee, 1997
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Level 4-1 / Sound Test Track 9: Shade Man's Stage Theme - Mega Man 7
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Level 4 End cutscene: Underground Theme - Super Mario World 2: Yoshi's Island
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Level 5: Bowser Theme - Super Mario 64
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End Credits: Sha-La-La-La-La - The Walkers
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2 Player Mode: Hammer Bros. Battle Theme - Super Mario Bros. 3
--- Found in code but unverified (looks like some of them are unused):
- "Sapphire City Act 1"
- "Dark Ambience"
- "mgzr7egb"
- All I Want - The Offspring
- Sonic Rush Adventure - Mystery Island