Advance Wars series - Sami's theme, Rachel's theme, and Grit's theme.
And, really, just about everyone else's: Drake's (at least in AW2, when the instrumentation was better), Colin's (ditto), Jess', Jake's, Sonja's, Javier's, Grimm's, Sensei's, Lash's, Sturm's, Kindle's, and Von Bolt's. And the Green Earth theme, for that matter. Just one of the all-around best soundtracks ever.
Castlevania series - Bloody Tears.
F-Zero series - Big Blue and Mute City.
Final Fantasy series -
From FF4: The boss theme and the fiends' theme.
From FF6: Celes, Terra, Relm, Kefka, Gogo, Cyan, The Decisive Battle, The Fierce Battle, Kids Run Through The City, Epitaph, Forever Rachel... probably 65+% of the soundtrack, really.
From FF7: Yuffie's theme, Jenova's theme, Rufus' parade, and Cosmo Canyon.
From FF9: You Are Not Alone, Vama'alla Flamenco, Beatrix's theme, and the instrumental version of Melodies of Life.
From the entire series: Theme of Love and the different chocobo variations.
Fire Emblem series - The main series theme, Together We Ride, Determination from FE8, and the dozen or so variations on Lyn's Theme/Eliwood's Theme/Hector's Theme/Recollection of a Petal/etc. in FE7.
Kirby series - Green Greens, Float Islands, Gourmet Race (the one in SSB games), the log raft level music from Kirby 64 and two or three levels in Kirby's Dreamland 3, and King Dedede's theme. Probably others that I'm forgetting; Kirby soundtracks generally rock.
Metroid series - Brinstar and the Tallon Overworld.
Pokemon series - Probably 50% of the soundtracks in most of the games.
From R/B/Y/FR/LG, basically every piece is quality. The battle music, gym battle music, Pokemon march theme (played on some of the later routes, like all the ones between Lavender and Fuchsia), Celadon City, and the St. Anne are particularly great.
From G/S/C, most pieces other than forest/cave exploration are quality--and even then, that one farm in the northwest corner of Johto has a nice tune. It's a shame that only a few of them were ported over to FR/LG.
From R/S/E, the music took a bit of a downturn and I'd be hard-pressed to identify a theme other than Slateport and the Regi battles that really stands out to me. Most is good, but somewhat forgettable and just not deserving of coming close to "favorites" like so many others.
Colosseum, for its many flaws, had an absolutely fantastic soundtrack from beginning to end and in every way. Every battle theme, Phenac City, Realgam Tower, Pyrite Town...
XD somehow had an even better soundtrack thanks to preserving most of the best Colosseum themes, then inventing more good battle stuff, a nice port town theme, an adventurous theme near the beginning, and the Purification Chamber music.
Ogre Battle - "Thunder" from the original SNES/PSX Ogre Battle stands out.
Legend of Zelda series - The Hyrule overworld theme, Kakariko Village, the Song of Storms, Outset Island, Dragon Roost Island, the Dark World Death Mountain in A Link to the Past, and the crystal maidens' theme (AKA Zelda's Lullaby since apparently nobody remembers that the music existed in LttP).
Tales series - Fighting of the Spirit from most of the games.
From Tales of Symphonia specifically, Colette's theme, Presea's theme, Sheena's theme, Full Force (the "first half" battle theme), the first world map theme, and the Flanoir scene music really stand out. Most of everything else ranges from good to amazing.
Meteos - The title screen theme. If only because it's hilarious to have something that RPG-ish in feel in a puzzle game.
Breath of Fire - Subpar game (and series), but both of the battle themes are top-notch.
Lunar: Eternal Blue - The second song (the one after you beat the Epilogue) and its instrumental variation that plays in certain towns.
Star Ocean: The Second Story - Theme of Rena and all of its variations (Lose One's Illusions at the beginning of the second disc, A Quirk of Fate at the end of the first, The Venerable Forest in forests, etc.), Dynamite (boss theme), KA.MI.KA.ZE. (Eluria Tower), Shower of Blossoms (Cross town), Stab the Sword of Justice (battles), Let's Walk in a Parade (Fun City), Cooking Master, Mission to the Deep Space (Cave of Trials theme), Star Ocean Forever (after beating the Cave of Trials), The Incarnation of Devil (Gabrie Celeste theme), In a Lightsome Mood (port town theme), and the Rescue operation (Salva Drift theme). Best soundtrack ever outside of SSBM, and even then I'm not sure.
Valkyrie Profile - The theme that plays when you're listening around the world for voices of the dying.
Mega Man X (I think it was the original) - Storm Eagle's level.
Tetris - Like I have to explain this.
Super Mario Bros. series - The SMB1 theme, the SMB3 theme, the SMW theme, the water themes from SMB1 and SMW, the SMB2 theme, the Yoshi's Island theme, the Mario 64 theme, and the Mario 64 water music.
Banjo-Kazooie - Bubblegloop Swamp and Rusty Bucket Bay.
Diddy Kong Racing - Darkmoon Caverns, Treasure Cove, and that one snow level with the loops that I can't remember the name of. Embarrassingly kiddy game, but the soundtrack had moments.
Star Fox 64 - The main theme that played at the end of most missions.
Chrono Trigger - Schala's theme, Crono's theme, Marle's theme, Frog's theme, Magus' theme, Robo's theme, the boss battle theme, the secondary boss battle theme, the multiple last boss battle themes, the 600 AD theme, the 1000 AD theme, the Epoch theme, the Kingdom of Zeal theme, the Millennial Fair, the Moonlight Parade, To Far Away Times (the ending theme)... yeah, basically everything.
Donkey Kong Country series - The main theme from DKC1, Jib Jig from DKC2 (the level where you're the snake the whole way through), and that Celtic-sounding pirate ship theme from DKC2 that I don't remember the title of.
Earthbound - Onett. Also Pollyanna, but was that in this game or just Mother 1 and SSBM?
Lufia 2: Rise of the Sinistrals - Boss battles, normal battles, the ending theme, the Mystic Stones theme, Portavia, and Lexis' lab. Sinistral battles is good, but not as high-tier as the rest.
Secret of Mana - Angels Fear, the happy town music, and the theme that plays in the snowy area.
Note that Dance Dance Revolution music is auto-disqualified mainly because I have no clue which of it is original and which isn't. Same reason Goldeneye stuff isn't on the list, really.
