Any Mega Man game
JoJo's Bizarre Adventure
Any Street Fighter game except IV
King of Fighters '95, '98, and '99
Final Fantasy IV and VII
All the Ace Attorney games
Persona 1 remake, Persona 3 and 4
Breath of Fire 1, 2, 3, and 4
Daytona USA
NiGHTS into Dreams
Sonic 1, 2, 3, and Knuckles
Sonic Adventure
Atelier Iris
Shining Force
Grandia 1, 2, and Xtreme
Final Fight
Strider 1 and 2
Super Smash Bros. Brawl
Kirby's Dream Land 3 (especially Zero's theme)
Kirby Super Star
Kirby's Adventure
Paper Mario
Mario Bros. 3
Yoshi's Island
Zelda OoT
Diddy Kong Racing
Mario Kart 64 and MKDS
Art of Fighting (only the SNES version)
Golden Sun
Dr. Robotnik's Mean Bean Machine
Super Hang-On
Outrun
Streets of Rage 1 and 2
The entire Darkstalkers series

I have to say, overall I honestly think Sega and Capcom has the best music in their games. Or at least had.