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.
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 soundtrack of one of the most popular mods Calamity for Terraria is also way too good than it ever should be