Uh, depends how far back you want to go. Ours was an Atari (ST) household, so a lot of the iconic games we enjoyed will simply be unknown to the console crowd (particularly the NES freaks who end up dominating discussions such as this), and vice versa.
Heck, a lot of the most memorable pieces of music from that era for me (and there are quite a few - the ym2149 sound is strangely evocative) came off of megademos and the like, which is a phenomenon that simply does. not. exist. in the console arena. Some of the best things Mad Max (Jochim Hippel) ever made, for example, were - at least initially - known to me through that route. (I've since learnt that one of my favourites of his - A Brief History Of Time - was actually the theme to some trashy platformer, and only later made it to demotown... bit of a waste, if only it had been picked up by the big players)
But let's have a think in the spirit of all this.
ST
Supercars (1) - which you could make a mini album of good tunes from, Fast Lane, the quite quiet and subtle background themeage of Mega Lo Mania, the bounciness of mario-wannabe Terry's Big Adventure, Xenon (1...) and ... ah, I've gotten too rusty since the machine itself broke down and I lost my emulator files. There were some titles that were cool just to load up for the music alone. Those are but a few.
Also the PD/coverdisc titles (i.e. NO ONE else will probably have heard of 'em) "Snacman" and "Tesserae" (go on, just guess what classics they were based on) were audio visual treats throughout. Not bad, if you consider the computer's dismal official specs.
(hmm, am I allowed Elite, and moreover Frontier, even though they only played classical pieces?)
Then eventually we got a Game Gear...
Sonic 1 ... good variety of good tunes in that. I once considered finding some way of getting the blue streak into a safe place on each level and taping the headphone output for independent enjoyment.
Streets of Rage does things with the sega PSG that may just make you cry.
and ... hmm. There weren't THAT many instances of good music on this platform for some reason, despite the above examples, and it having something that was probably a very close YM relative. Not many horrors, but not too many standouts either. Merely adequate.
(Defenders of Oasis starts out well, with a solid title theme, but once you've heard the overworld or battle music loop for the seventy trillionth time... ugh)
After that, a PC and the big wide world of emulation, with everything melding into each other.
Whereupon, after a brief fling with the C64 (Outrun FTW), we discovered FF5 and 6 on the SNES, and all bets were immediately off.
(Oh yeah, and Worms... ok I know it was on PC CD-ROM, but given it's now 15 years old (age-check: we used C64 and ST emulators a lot because neither the machine had enough power to emulate 16-bit consoles very well, nor had the state of available emulators progressed enough to offer a good experience), is it allowed to be included? 15 years before that, the home computer/console market practically didn't exist. And the composer did bring some fun 16bit sensibilties to both the ambient and thematic pieces for what, essentially, was a very slightly souped up Amiga/ST game)
Eventually a game boy. Tetris of course, and Zelda:Links Awakening. But on getting a knockoff multicart, my favourite on that system immediately became, and remains Bombjack. Only like four short little tunes, but expertly crafted. And in stereo!
Fun fact. The whole world doesn't know the mario theme. I myself only really learnt it on getting that multicart (late 90s). Just wasn't exposed to it enough, or very early. Early Nintendo systems really didn't make anything like the headway in europe as they did in the states or japan. Too expensive for a start. Our world was of 6502/Z80/68000-based keyboard computers, or (cheaper!) Segas.