Panzer Elite Action was quite crappy, but the soundtrack was surprisingly good. This can be explained by the fact that it was not composed for the game itself but was made by 2 composers (Terry Devine-King and Ian Hughes) who make all kind of music that they sell on a website to anyone who want it for their project : https://www.audionetwork.com/
So the game's developers bought the rights of the music for their game rather than make it themselves and.... well, they probably were right on this one ! :p

Here is one from Terry Devine-King : https://www.audionetwork.com/browse/m/track/exploration-b_14536
And one from Ian Hughes : https://www.audionetwork.com/browse/m/track/promised-land-3_1036

The music actually seems to be a bit out of place in this game. ^^

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Outlaws also had an awesome soundtrack by Clint Bajakian (heavily inspired by the works of Ennio Morricone). The game wasn't that bad, but it was already obsolete when it came out in 1997, using the build engine of Duke Nukem 3D while Quake 2 was already out.

Action 52 (NES, unlicensed) actually has some decent music, at least when the music works correctly.

For example:
Lollipops level 2 has a decent music track, albeit too short. (Of course, level 3's music is a glitched mess.)
Haunted Halls level 3's theme is odd, and might be suitable for people who like avant-garde music. (That is, when it doesn't glitch up.) With that said, this one isn't for everyone. (It might qualify as aleatoric due to the fact that the melody isn't synchronized with the rest of the track.)
Evil Empire has a decent theme song.
And, of course, the Cheetahmen theme could be considered famous. (I note that Syoban Action, also known as Cat Mario, uses part of this theme for the outside levels, though the difference is that Syoban Action isn't a bad game if you don't mind games with lots of unfair traps.) I could point out, however, that the music doesn't properly loop, resulting in the melody being absent when the music repeats. (There are a decent amount of remixes of this theme out there.)

Ultima 5 (NES version) manages to have one good music track; unfortunately, it's not the one that plays for pretty much the entire game. (It plays during the intro (including the questions you have to answer) and the ending.)

This is just games that are generally considered bad by nearly everyyone familiar with them. (Note that other versions of Ultima 5 aren't bad; it's just the NES version that is.) If, however, you consider games that I consider bad, but which other people seem to like for some strange reason, I could add Final Fantasy 7; the theme when you ride a chocobo (5/4 jazz remix of the chocobo theme) is my favorite version of the chocobo theme, and the final boss music is quite good (even if the fight drags on unnecessarily due to the boss having an attack with a (literally) 2 minute animation).

Edit: Back to Action 52, I noticed that the Youtoube video for the Slashers level 2 theme says "NOTE: This song plays slightly differently every time you start this level.". That should tell you something about how well (or rather poorly) the game was coded.

I love David Bowie's title song from "Omikron -The Nomad Soul", but I didn't really like what few I saw of the game. Very clunky controls in the action parts, inconsistencies in the adventure game parts. Still, that soundtrack ...

IMHO, Sonic the Hedgehog 2006's soundtrack is every bit as good as the rest of the game is not.

The hell is wrong with GOG's URL syntax? If I try to add more than one link it completely implodes.

Oooh I remember when I was making worthwhile posts and thread. But, three years ? I thought it was much longer ago.

And apparently I hadn't watched Pacific Rim yet.

Despite its flaws I think the game is worth playing, the gameworld is really unique, if I had to make comparisons it's like Anachronox meats Zeno Clash.

I tried, and I really wanted to love it, but I couldn't.

Spyro: Enter the Dragonfly. One of the games I got when I was given my first PS2 when I was a kid. I grew up playing the first three Spyro the Dragon games and loving them endlessly. The worlds, the gameplay, the fun characters and, of course, the excellent soundtracks by Stewart Copeland. So you can imagine the genuine displeasure of booting up Enter the Dragonfly only to be "gifted" with painfully long load-times, excruciatingly slow gameplay and bugs and glitches galore. And listening to a couple of the songs just now, I can't help but feel that the awesomeness of Stewart Copeland's music was wasted on this unfortunate mess of a game. *sigh*

Not necessarily terrible games, but ones where the music far outshines the gameplay.

1990:
Captive (AMI)
Leavin' Teramis (AMI)
Silver Surfer (NES)
Unreal (AMI)
Lost Patrol (AMI)
Zeliard (PC, MT-32)
​Mouryou Senki Madara (FC, VRC6)
​Shadow of the Beast II (AMI)
​Ys III (X68K)
​​Killing Game Show/Fatal Rewind (AMI)
Rogue Trooper (AMI)
Hole Chaser (PC-88, OPNA)
​Sorcerian (PC, MT-32)

1991:
Starblade (ARC, YM2151)
​Solvalou (ARC, YM2151)
​Hero Quest (NES (unreleased) & Atari ST)
Utopia (AMI)
Alien Breed (AMI)
Genocide 2 (X68K, MT-32)
​E.D.F.: Earth Defense Force (ARC, YM2151)
Pegasus (AMI)
The First Samurai (AMI)
Gods (AMI)

1992:
Spider-Man & X-Men: Arcade's Revenge (SNES)
Robocop 3 (C64), Robocop 3 (NES)
Project X (AMI)
Zool (AMI)
Assassin & Assassin: Special Edition (AMI)
Utopia: The Creation of a Nation (PC, MT-32)
Devilish/Bad Omen (MD)
​​Super Off Road (SNES)
Lethal Enforcers (ARC, K054539)
​Harlequin (AMI), Theme
​Dragon Slayer: The Legend of Heroes II (PC-98, OPNA)

1993:
Plok (SNES)
Body Blows (AMI)
Breath of Fire (SNES)
TFX: Tactical Fighter Experiment (PC, MT-32)
3 Count Bout (NG, YM2610)
Space Hulk (AMI)
Gauntlet IV (MD)
Run and Gun/Slam Dunk (ARC, 2x K054539)
Retee 2/European Champions (AMI)

1994:
Body Blows Galactic (AMI)
Thoroughbred Breeder II (SNES)
Eek! The Cat/Sleepwalker (SNES)
J.R.R. Tolkien's The Lord of the Rings, Vol. I (SNES)
Nobunaga no Yabou: Tenshouki (SNES)
Vortex (SNES)
Super Stardust (AMI)
Time Trax (MD, unreleased)
Lethal Enforcers II (ARC, 2x K054539)
The Smurfs (NES)
​The Lawnmower Man (SNES)

1995:
Alien Virus (PC, SB Wav/Mod?)
Hi-Octane (PC, SB AWE64)
​Waterworld (SNES)
FX Fighter (PC, SB Mod)
The Flintstones (SNES)
Future Dimension (PC, SB Mod)
​Classic Road II (SNES)
Road Rage/Speed King (ARC, K054539)
Foreman For Real (SNES)

To be continued!

1996:
Grounseed (PC-98, OPNA & OPN)
In Pursuit of Greed (PC, SB Mod)
Kono Yo no Hate de Koi wo Utau Shoujo YU-NO (PC-98, OPNA)
Piranha (PC, SB AMF Mod)
KOPS (PC, SB Mod)
Kara no Naka no Kotori (PC-98, OPNA)
Watchtower (AMI)
Winter Gold (SNES)
Die Hard Trilogy (PS1)
Tobal No. 1 (PS1)

1997:
Iron & Blood: Warriors of Ravenloft (SB Wav/Mod?)
Turok: Battle of the Bionosaurs (GB)
Kirby's Dream Land 3 (SNES)
Flying Squirrel (X68K, YM2151)
Sila's Quest (PC, SB Mod?)
Vanguard Ace (PC, SB Mod)(in-game)
The Smurfs' Nightmare (GB)
Shigesato Itoi no Bass Tsuri No.1 (SNES)
GaoGao! 4th Canaan: Yakusoku no Chi (PC-98, OPNA)
Fourth Generation (PC, SB Mod)
Hugo 2 (GB)
Croc: Legend of the Gobbos (PS1)
Outlaws (PC)

1998:
Love Escalator (PC-98, OPNA)
Turok 2 (GB)
Heisei Shin Oni Ga Shima Parts 1 & 2 (SNES)
Mini Yonku Let's & Go!!: Power WGP 2 (SNES)
Ring ni Kakero (SNES)
V-Rally (GB)
Heiwa Parlor! Mini 8: Pachinko Jikki Simulation Game (SNES)
Brave Fencer Musashi (PS1)

1999:
Kirby's Super Star Stacker (SNES)
Tamagotchi Town (SNES)
Famicom Bunko: Hajimari no Mori (SNES)
Final Fantasy VIII (PS1)
Castlevania 64 (N64)

Do we have good soundtrack games. I wish to nominate one, but I think it's actually great game with lovely soundtrack.

Yes, here for example: https://www.gog.com/forum/general/which_are_your_favorite_games_soundtracksindividual_tracks