PSX:
-Crash Bandicoot (1-3)
-Ace Combat (2-3)
-Gran Turismo (1-2)
-Tony Hawk Pro Skater 2
-Tekken (1-3)
-NFL Blitz (Much lighter on the rules, so dogpile the QB after sacking them)
-Tomb Raider (1-3) (1 was great, 2 was intense, 3 is ‼fun‼)
-Moto Racer
-Cool Boarders (2-3, 2 is a personal classic)
-Parasite Eve
-Metal Gear Solid
-Raystorm and Raycrisis
-Intelligent Qube (I.Q. for short)
-Frogger (2)
-Armored Core (Since you like mech games)
-Steel Reign (Tanks tanks tanks)
SNES:
-Chrono Trigger (There's a re-translation patch out there too)
-Battle Clash and Battle Clash 2: Metal Combat (might need ZSNES to use the light scope (via mouse))
-Mega Man X-X3
-LoZ: Link to the Past (Personal Classic)
-Super Bomberman (for multiplayer mayhem and fun)
-Secret of Mana
-Breath of Fire
-Super Metroid (Best of the Metroid games)
-Blackthorne
-Flashback: Quest for Memory (There's a decent
remake on Steam as well; more up-to-date, and a bit more story to it)
-Another World/Out of This World
-Super Mario RPG
-2020 Super Baseball (Surprisingly addictive)
-Donkey Kong Country (1-3)
-F-Zero
-Front Mission
-R-Type III
-X-Zone (Another Super Scope game)
-Yoshi's Island
GBA:
-Castlevania: (Dawn/Aria?) of Sorrow (and Harmony of Dissonance)
-LoZ: The Minish Cap (and backwards compatibility, Oracles of Ages and Seasons, and maybe Link's Awakening)
-Shantae
-Metroid Fusion and Zero Mission
Descent (2) does play way better on PC, and there are Direct3D/3Dfx patches that plays it on higher resolutions too. Plus, I advise remapping the keys to work WASD for lateral and vertical strafing (or WS for forward/backward movement, and QE for up/down strafing), and the ↑↓→←→ (or keypad) keys for turning. Shift for alt-fire, and space for primary fire. It'll take a moment to get used to, but it's the most intuitive setup I've got to navigate via keyboard as I see fit. Extremely helpful for getting out of a level quick post-reactor destruction.
Since I'm suggesting PC ports, I also suggest Mechwarrior 2: Mercenaries for PC. Nothing like a custom PPC-riddled mech to blast other mechs to kingdom come. I love my Warhawk-custom. It's slow, but powerful. It's also fun taking out 50-story mechs in an Elemental Battle Suit.