First off, there is no picking "one" (unless you mean one system, then I'd go with Super Nintendo). Secondly, I don't know what constitutes "old school" anymore, much less what those reading this would consider it to be, so I'll just stay away from current gen consoles/games:
Atari: Pitfall, Centipede, Frogger, Qbert, Breakout, Dig-Dug, Space Invaders
Caleco Vision: Burger Time, Galaxian, Choplifter,
NES: Metroid, Kid Icarus, Super Adventure Island, Zelda, Mario 3, Contra, Gradius
Gameboy: Super Mario Land, Tetris, Pokemon Red/Blue, Metroid II: Return of Samus
Atari Lynx: Crystal Mines II, Lemmings, Super Asteroids and Missle Command, Rampage
Sega: Sonic (any), Altered Beast, Bomberman
Super Nintendo: TMNT Turtles in Time, Street Fighter II, Super Mario World, Super Scope 6 (bundle), Donkey Kong Country, Secret of Mana, EVO: Search for Eden, Zool, F-Zero, Bill Laimbeer's Combat Basketball, Sim Ant
PS1: Resident Evil, Crash Team Racing, Tony Hawk's Pro Skater, Tomb Raider, FFVII, Parasite Eve, Twisted Metal
Atari Jaguar: Alien Vs Predator, Primal Rage
N64: Goldeneye (was there any other games?)
Gamecube: Pikmin, Wave Race, Phantasy Star Online
Dreamcast: Soul Caliber, Crazy Taxi
Sega Saturn: Die Hard Trilogy, F1 Racing
PS2: 007: Agent Under Fire, GTA: San Andreas, FFX, God of War (all), Need for speed (all), Tekken (all), Resident Evil (all), Devil May Cry, Max Payne, Twisted Metal Black
Xbox: Halo, TESIII: Morrowind, Fable
Xbox 360: Army of Two, Prototype, Forza, Turok
Wii: Super Smash Bros Brawl, Wii Sports, Zelda: Skyward Sword/Twilight Princess,
PS3: CoD Blops II, Uncharted (all), Resistance: Fall of Man, Resident Evil (all), inFamous, DCUO, Skyrim
PC: Oregon Trail, Team Fortress, WoW, Lotro, Starcraft, Spore, Zombocalypse, HRmageddon, Wolfenstein, Doom, SkiFree, Age of Empires (all)
I am absolutely leaving out a ton of games, and likely a system or two, but these just spring to mind.