I have a few answers, but I agree that Chrono Trigger is one of those games you come back to again and again. I think there are many excellent games which wouldn't qualify because they are too firmly rooted in their time, or perhaps don't feel timeless due to the limitations of their interface, but here are a few titles that are not just my favorites but I also think compare boldly across systems, genres, and time. I may have got carried away :|

edit: formatting, I'mma Lemmy newb

Sega Master System

• Columns: the best iteration of this tetris-esque game series imo
• Choplifter: what a brutal, unforgiving game, and you feel so horrible when you crush people you're trying to save

Sega Genesis

• Samurai Showdown (Genesis): A fighter oozing with personality, weapons, and a good balance of combos, strategy, and special moves that reward you just enough to want to learn that next move without feeling like you can just mash buttons

PC Engine / Turbografx 16

• Ninja Spirit (PC Engine): hard as hell, but also cool as hell
• Devil Crush: ultra-stylish, demonic pinball
• Blazing Lasers: OK, this one might be an easier title, but it's so much fun to cause so much carnage, and the layered parallax backgrounds are lovely

NES

• Ninja Gaiden: I still haven't beat it, but I can't not keep trying
• Kirby's Adventure: what a charming, vibrant world

SNES

• Super Street Fighter 2 series: gold standard fighter
• Earthbound / Mother 3: a unique, unusual, and psychedelic RPG
• Zombies Ate My Neighbors: wacky, stylish top-down mayhem with an excellent responsive control and fun music
• ActRasier: Interesting cross of management and platform game where you play a deity manifesting to take care of its people against monsters and famine alike

PSX

• Castlevania, Symphony of the Night: Beautiful gothic horror metroidvania-action-rpg with great music
• Tony Hawk's Pro Skater 2: killer moves, combos, wipeouts, and soundtrack

PS2

• Guitaroo Man: Wacky superhero/superrockstar rhythm game supreme
• Katamari Damacy: obsessive, rainbow-splashed fun and mayhem
• Grand Theft Auto: San Andreas: my favorite title in this series

Xbox

• Knights of the Old Republic 1 and 2: Bioware RPG storytelling and environments at their finest
• Psychonauts: a stylish and funny masterpiece by Doublefine (except that fucking meat circus, ugggggh)
• Jet Set Radio Future: a vibrant, cell-shaded wonder in unmistakable sega style
• The Chronicles of Riddick: Escape from Butcher Bay: a surprisingly tight, atmospheric, and narratively compelling stealth game

PC

• Doom 1 and 2: well yea
• Minesweeper: man, I sill get sucked into this game
• Grim Fandango: a heartwarming and funny point-and-click noir adventure about death and a life worth living, beautifully styled after Mexican day-of-the-dead visuals and themes
• The Hitchhiker's Guide to the Galaxy: you may think you know what a text adventure game is, but this game will expand your mind
• Minecraft: OK, there are a LOT of versions and updates to this game, and it has become so complex, but whether OG vanilla or latest edition, there is nothing like loading up a clean, new world to explore, survive, and shape in new and exciting ways####___