Well, this thread can easily be summed up by the title itself.
As most of the time, the people responsible for making video game music tend not directly be responsible for making everything else. So it's highly possible a bad game may have a really good composer in charge.
As for my example. Pictionary on the NES, it's a LJN game, so you can already imagine the quality. But the music is probably the best stuff you'll hear on the console. I'm not even joking.
Anyways, post some examples if you want.
For a mediocre licensed game. This theme is considered a C64 classic.
derp sonic 06 dorp
But actually yeah probably most Sonic games? They tend to be mediocre to bad but hot-diggety-damn those soundtracks are almost always awesome.
Also the recent Paper Mario games, while they're not the best, they've at least got some jazzin' tunes to listen to.
Golden Sun and Final Fantasy 7. Those games are highly overrated, but even I can't deny the quality of the composers.
I would say Paper Mario Sticker Star has AMAZING music imo
I would have to say Streets of SimCity. The game itself is buggy and nigh impossible to play on modern systems, but you have to admit, it had a pretty awesome soundtrack.
Hotel Mario has some pretty good music, like the credits theme:
And the battle theme from Paper Mario: Sticker Star is also pretty good:
Rise of the Robots on the SNES has a rockin' soundtrack, and also Timecop.
People have already brought up modern Paper Mario, I second that, the music is the one thing that didn't fall off imo.
But may I draw attention to SpongeBob SquarePants: Supersponge. It has an absolutely magical soundtrack despite being objectively a mediocre-at-best licensed game. I myself grew up with the GBA version, which compressed the music and made it sound significantly worse, but listening to the PlayStation soundtrack years later it still felt like my childhood came rushing back better than ever.
And while the GBA version's compression mutilated a lot of the soundtrack, listening to the ripped MIDIs bypasses that and lets us hear how they were meant to sound.
Still not as grand as the PS version, but a more pleasant version than what it sounded like farting out of a GBA's speakers.
I'd say Battle Arena Toshinden. Kinda mediocre 3d fightan (then again, what 3d fighters AREN'T mediocre), but hot damn they got some of the best soundtracks i've ever heard.
I think Castlevania Judgment fits this category.
While Sonic the Hedgehog 4: Episode 1 doesn't have the best music, there are a couple songs I kind of like.
Casino Night Street Zone (Act 1) is probably one of the more "memorable" songs in the game (to me at least).
The title theme might not be as good as the song I previously mentioned, but at least it's better than Splash Hill's music.
Street Fighter II on Gameboy is 1 example
Finding Nemo for the GameCube is just an average licensed kids game, pretty bad but the soundtrack is great.