Hey very nice idea, and you put it well in your introduction. I'm an old gamer, so my choices start from the mid 80's. I'm not sure how much playable they are today, but I think that games like OutRun, Bomb Jack, Defender of the Crown, Green Beret (Rush 'N Attack in the USA) and Monty On The Run were great and very fun to play.
I wasn't gaming at all in the 90s, at least not until 1998, so my picks from this era will be: Command & Conquer: Red Alert, Final Fantasy VII, Castlevania: Symphony of the Night, Silent Hill, Tomb Raider (1-4), Resident Evil 2, Metal Gear Solid, Gran Turismo, Broken Sword and Civilization II and III.
From the early and mid 2000s, I would propose: Baldur's Gate: Dark Alliance, Shadow of Memories (I think it's Shadow of Destiny in the USA), Metal Gear Solid 3: Snake Eater, Silent Hill 2, Resident Evil: Code Veronica X and Resident Evil 4.
From the late 2000s until today: World of Warcraft, Uncharted: Drake's Fortune, BioShock, Call of Duty 4, inFamous, Demon's Souls, Fable 2, Dead Rising 2 and Dark Souls.