Here we go. I'm leaving out the systems I can't really comment on. Also, I'm not going after the best titles so much as the ones that seemed the best specimen for that system.
Atari 2600 - California Games (I was late to the party, but that title screen looked like something from the C64 demo scene)
Intellivision - Major League Baseball (two players, puts all the controls to use)
Vectrex - Pole Position (arcade classic, timing trick to "bend" the vectors, and puts the analog functionality of the original joystick to subtle use)
Colecovision - Donkey Kong (if you've played one CV game, you've pretty much played them all, so this one is the most iconic)
Atari 7800 - Ballblazer (something that doesn't sound like ye olde 2600)
Sega Master System - Missile Defense 3D (maybe I should have left this system out; I went with something that put two hardware peripherals to use)
NES - Super Mario Bros. 3 (probably needs no introduction)
Sega Genesis - Sonic the Hedgehog 3 (really the whole trilogy plus Sonic & Knuckles, but this one stood out the most)
Game Boy - Tetris (What else? Puzzle games were what the Game Boy did best)
Atari Lynx - Blue Lightning (so awesome it was made into a store demo)
Turbo Grafx 16 - Bomberman (5 players was a first here)
Sega Game Gear - Sonic the Hedgehog 2 (made the system look like more than a glorified SMS handheld)
SNES - Yoshi's Island (let's be honest; most games were just 2D platformers and not the "Mode 7 showcase titles" they could have been)
3DO - Return Fire (one of the few games that made the system look like more than a CD player with game hardware tacked on)
Sega CD - Earthworm Jim (popular on other platforms, and had a bonus level!)
Atari Jaguar - Tempest 2000 (probably the only released game that deserves any recognition)
Sega 32X - Knuckles Chaotix (put the hardware capabilities to use once in a while, and was probably more fun than most other titles)
Jag CD - Vid Grid (surprisingly fun considering it's a pack-in title, and it's also surprising that Blue Lightning and Myst weren't better)
game.com - Henry (that and Lights Out were the only games that really did it justice; everything else was a joke, including Resident Evil 2)
Virtual Boy - Red Alarm (killer app, and also put both D-pads to use)
Sega Saturn - NiGHTS: Intro Dreams (a quirky 3D game that takes a little getting used to, demonstrates that Sega is making some effort to be innovative during this period)
N64 - The Legend of Zelda: Ocarina of Time (put Zelda back on the map; if I cared about hardware peripherals, I would have gone with Majora's Mask)
Dreamcast - Crazy Taxi (just plain fun, as games ought to be)
Nuon - Tempest 3000 (Yes, I have one. Shut up.)
Game Boy Advance - Castlevania: Circle of the Moon (a fine specimen of the early units; you had to play in direct sunlight)
GameCube - Luigi's Mansion (The C-stick is analog? Coulda fooled me!)
PlayStation 2 - Gran Turismo 3 (brilliant graphics, and puts to use that silly Firewire port on the front of the early units)
Wii - Wii Sports (What else comes first to mind for most people?)
Wii U - Nintendo Land (one of the few Wii U titles worth mentioning)
Nintendo Switch - Super Mario Odyssey (Breath of the Wild would have been the "killer app" the Wii U desperately needed; this game really feels like a Nintendo Switch title)