Here listed are games with music I like, and some standout tracks from each.
I think all the Dragon Quest games on SNES have really evocative soundtracks, even I and II, there's something so quaint, yet grand about the way the small instruments are orchestrated. Good echoey sounds.
I - Overworld
III - Prologue
VI - Town
Drakkhen has a pretty weird soundtrack, but there are some really relaxing and interesting tunes in it. Has that early SNES vibe to it. I find early SNES game tunes using stock sdk sounds to have really fun music! (Super Mario World, SimCity, Pilotwings etc.)
House in Air Area
Staff Roll
SimCity - Budget
The JP exclusive Nintendo published games on SFC have good music too! Sutte Hakkun and Marvelous: Mouhitotsu no Takarajima are ones that come to mind.
Sutte Hakkun - Stage 6
Sutte Hakkun - Stage 9
Marvelous - Gina
I'm a big fan of Kentarou Haneda's music composed for Wizardry, and he certainly does not miss on the SNES ports of Wizardry V and VI, they both have a very classical vibe to the music, with Wizardry V almost sounding like a film score at times, and Wizardry VI having more ambient and immersive tracks while still having score-like tracks.
Wiz5 - Title
Wiz5 - Inn
Wiz6 - Dungeon 1
Both the Uncharted Waters games on SNES have very cozy seafaring tracks done by Yoko Kanno, although the first game I will admit is an acquired taste, with the simpler and sometimes detuned sdk instruments, though I like it. The second game however, has really good music with great piano sounds and latin/jazz elements!
1 - Occidental Port
2 - Wind Ahead
2 - Empty Eyes
As a really big Puyo Puyo fan, I've played the crap out of almost every Puyo game, which includes the SFC games. I would say for normal listeners, Super Puyo Puyo 2 has better music than Super Puyo Puyo 2 Remix, because Remix has kind of crusty instruments, but for some reason, I really prefer the crusty, detuned, sound that the Remix version has. It tickles my brain in a funny way. The spinoff Nazo Puyo games also have fun tracks with a lot of variety.
Area B -
2 Remix
Area C -
2 Remix
Nazo 2 - Intro
For you fans of Earthbound music wishing for more, I recommend Snoopy Concert, a JP exclusive Peanuts game for SFC that has some fun tracks, with a familiar sound to them. Hirokazu Tanaka worked on the music for this game, as well as Earthbound.
Pine Crest Elementary
Theme of Linus
Theme of Peppermint Patty
For a cute, silly, and overall jolly vibe, I really dig the soundtrack to Motteke Oh! Dorobou, a SFC game by Data East, which is full of fun-spirited tracks. The game itself is kind of like a board game centered around stealing and heists, but there is no translation and no .spc rips of the soundtrack for some reason, so I don't know where most of the songs play.
Overview
Board
???
Lord of the Rings on SNES is a boring game, and not a good adaptation of the source material, but it has some absolutely epic music. I even like the Moria themes and the stuff that is more on the ambient side, it's pretty immersive.
Title
Town
Nazghul
and a bonus!!!!
The Might and Magic III soundtrack for Super Famicom! An unreleased Japanese localization of the game was planned, but it was ultimately canned, and recently a YouTube channel by the name of Xeen Music miraculously managed to upload recordings of the soundtrack from the composer, Takeshi Abo, and the music is awesome! I truly think if the game was released, a lot of video game music enthusiasts would be listening to it. Sadly, probably will never see the game or a .spc rip of the soundtrack, since it is ultimately lost to time.
The Playlist on YouTube