• The whole set of NES Mega-Man games had amazing soundtracks, although 2 is the best. There’s barely a story there, but the gameplay is solid.
• Final Fantasy VI has Dancing Mad, and that alone would be enough, but the whole damn thing is just amazing, especially the Opera.
• Similarly, Final Fantasy VII had a stellar soundtrack, including the holy-shit-this-is-amazing One Winged Angel.
  • All Final Fantasy games have great soundtracks, but these two are my faves
• Someone mentioned Terraria, and I would be remiss if I didn’t second it. Not much story there, but I’ve been playing it for like 12 years and I’m still happy every time I start it up.
• The Elder Scrolls games from Morrowind on all have bangin’ soundtracks. Oblivion had the best one (although Morrowind and Skyrim are both better games, IMHO).
• Tempest 2000 for the Atari Jaguar of all things had a phenomenal soundtrack. Seriously, it it was one of the first games in the US to have its soundtrack sold in stores. And it stands up.

I’ll add more if I think of them. Most of the others I can think of have already been mentioned.

ETA:

• Chrono Cross, I can’t believe I forgot it! That OP is unforgettable, and yet somehow I managed to forget it! The game itself pales in comparison to its predecessor (Chrono Trigger, which also has a great soundtrack), but it’s not bad.
• On a similar note, the original Wild Arms had an excellent soundtrack with a western theme. Actually, the whole Wild Arms series has good music, but I just couldn’t get past one of the main mechanics that showed up in 2 and stick around.
• Another one I can’t believe I forgot, Nights: into Dreams had the best soundtrack on the Sega Saturn. It’s just perfect for the game, not a bad tune in there.