Patient Gamers

A lot of great ones have already been mentioned: (Old School) Runescape, Bastion, Bomb Rush Cyberfunk, Braid, Castlevania: Symphony of the Night, Celeste, Chrono Cross, Chrono Trigger, Crypt of the NecroDancer, Cyberpunk 2077, Deus Ex (2000), Donkey Kong Country 1 and 2, Doom 2016, Earthbound, F-Zero GX, FTL, Hades, Halo, Hi Fi Rush, Hotline Miami, Jet Set Radio and JSR Future, Kirby (any of them), Legend of Mana, Mother 3, Neotokyo, Nier: Automata, Pizza Tower, Quake, Ratchet & Clank (any of them), Risk of Rain 1 and 2, Shadow of the Colossus, Shantae (any of them), Shatter, Shovel Knight, SimCity 3000, Sonic 3 & Knuckles, Sonic Adventure, Sonic Adventure 2, Sonic CD (Japan), Sonic Mania, Sonic Rush, Stardew Valley, Tower of Heaven, Transistor, Trine, and VVVVVV

Here's some that haven't been mentioned yet:

Ape Escape

• PS1 game, soundtrack by icon of the 90s era Japanese House music scene, Soichi Terada. All of his tracks are bangers. I've seen the soundtrack described as House, Jungle, and DnB. Probably my favorite game soundtrack ever, but that's probably nostalgia talking.
• Soundtrack: Game Rip, Fan Remastered or Originape Soundtrack/Official Soundtrack CD (Note: Terada has released his own remastered tracks in the 2020s since the Originape CD, but they are split over multiple albums and I'm too lazy to track them down at the moment)
• Standout tracks: Peak Point Matrix/Galaxy Monkey, Primordial Ooze, Thick Jungle- Woods, Dark Ruins, Crumbling Castle, Specter's Factory- Outside, Time Station

Final Fantasy Legends III / SaGa 3 Jikū no Hasha: Shadow or Light

• Originally on Gameboy, Japan only remake on DS (fan translation patch exists). This is really a game in the SaGa series, but was released under the Final Fantasy name internationally for marketing purposes. Characters don't have levels, their stats change based on what they do. Enemies also drop meat and parts that you can apply to a character to change their class, with some unique mechanics for different types. Features a time traveling stealth bomber, THE TALON, that may possibly be the only airship in gaming with a working toilet. DS Remake is generally better, but it kills overworld exploration by turning it into "select an adjacent POI" instead of free roam.
• Soundtrack: Gameboy, unfortunately I can't find this version with track names. DS Remake
• Standout Tracks: Setting off into the future, Holy Ruins (a criminally underused track in game), Oasis (has some odd animal sfx added in the middle in this remake version), Stronghold (imo, one of the best dungeon themes in gaming), THE MOTHERFUCKING TALON THEME (this is the GB version, as the DS remake loses the countermelody which imo weakens the track)

Ghost Trick

• Originally for DS, has been remade for just about everything now. It's effectively a VN with fancy gameplay segments, and the music really helps carry the whole thing. Beautifully done sprite animation too.
• Soundtrack: DS, 2023 Remaster
• Standouts: Ghost Trick, Lynne- Red-Headed Target, Awakening, The Mystery Surges Ahead, Cabanela - Lanky and Loose Lawman, Jowd- Fated Jailbird

Gunpoint

• Old indie sidescrolling noir stealth game. The main gameplay revolves around puzzle solving by hacking buildings' electrical systems. Hook that lightswitch up to the secure door lock. Rig that motion sensor up to short out a power plug and take out a guard instead of it just turning on the lights. Delightful jazz soundtrack.
• Soundtrack
• Standouts: Security, Circuitry and You, Subterfuge Shuffle, Cold Halls and Footfalls, The Five-Floor Goodbye

Megaman ZX

• DS sequel to the Megaman Zero series for GBA, but now with a Metroidvania twist.
• Soundtrack: ZX Tunes- Official remix/rearrange soundtrack
• Standouts: Innocence- 90s style anime opening, Green Grass Gradation, Rockin' On, Brilliant Show Window, Cinq Ville - C`est Notre Espoir, Gauntlet

And I've spent way too much time on this comment. Here's more not mentioned so far that I don't have time to do a writeup for: Skies of Arcadia, Super Meat Boy, Tomba 2: The Evil Swine Returns, Uplink, XCOM (Original), XCOM (Reboot), XCOM 2 (Reboot)