Okay, I think I'm fairly well versed in this area, hahah.
First off, I'm going to cheat a little, by using music that came out in 1990, but damn is it worth it.
Journey to Silius, a moderately good game with an amazing soundtrack. What's really amazing is that the entire collection of songs is fantastic, with huge dynamic range, decent length, incredibly detailed use of the minimal NES sound channels, and more.
Another 1990 game (the last of my list), Silver Surfer was well known for being frustratingly difficult, in a bad way. However, Tim Follin was brought in for the soundtrack, and his work is well known. He is probably the most talented chiptune composer of the period, able to make music that many would think impossible on the standard NES channels. As such, this soundtrack is also quite amazing, although the selection of songs are short. Check out other things Tim Follin has worked on as well, they're almost invariably fantastic, regardless of the system.
Moving on into proper 90's music, we have DKC2's incredibly famous Stickerbrush Symphony. Remixed a billion times for good reason, the soundtrack has an incredible medley and atmosphere that fit the stages it was placed with. Like most of DKC2's songs, it makes a lot of use of PCM audio to expand the available instruments the SNES could provide, especially with drums and piano.
Pokemon's got a long history, and it's also got a lot of hit songs. However, this one in particular (Especially this VERSION of the song, as its medley has been reused several times) has always stuck with me. While Pokemon Red/Blue was the origin, this version adds in a strong bass line to parts of the song, giving it that extra punch. It really captured the atmosphere of the adventure and anticipation of the gym fights. Most Gameboy games have very short songs, and this is no exception, but it's powerful enough to stay on my VG music playlist.
1992, believe it or not. Kirby's Dreamland had a number of great songs, but overall, it was the unique sound they all shared that made Kirby's soundtrack iconic. While numerous games tried for the happy, airy soundtrack (even Mario), Kirby really nailed it.
It had to show up eventually, right? Sonic 3's soundtrack is truly legendary, with rumors (possible corroborating stories recently coming to light on this, lending credence to them!) of Michael Jackson participating in it's creation. While Ice Cap Zone is certainly the song most people first choose when mentioning this game, most of the songs in the game were in fact outstanding. The percussion and overall driving rhythm of the song really gave it a ton of energy, when the medley itself is actually quite slow. This game, like many games near the end of a console's lifespan, made heavy use of PCM to fill in the missing instruments. Drums were used nearly everywhere, but also, the game featured short voice clips as well. It wasn't the first time voices were heard in a game, but it was used so prominently and tastefully in Sonic 3 that I'll always remember it.
Anyway, I'll stop there for now, even though there's plenty more I'd love to touch on.