So go to your game collection and find some of the oldest games you can find.
Here are mine:
1. NES~ Zelda 2: Adventure of Link - 1987
2. GameBoy ~ Tetris - 1989
3. GameBoy ~ The Hunt for Red October - 1990
4. Nintendo 64 ~ Banjo Kazooie - 1998
5. Gameboy Color ~ Super Mario Bros Deluxe - 1999
I'm not sure of what the oldest one is, but it's most likely one of my NES games.
The ones I have are Super Mario Bros/Duck Hunt, Super Mario Bros 3, TETRIS, TMNT3: Manhattan Project, JACK NICKLAUS GREATEST 18 HOLES OF MAJOR CHAMPIONSHIP GOLF, GOLF, GOAL, and Adventures of Tom Sawyer.
I'm thinking it's probably SMB/DH, but I'm not really sure and don't really feel like researching.
I used to have a Game & Watch: Donkey Kong, which was released in 1982.
I'd say that my oldest games now are the ones in my SNES-collection. Super Mario World was released in 1991 so probably that one then.
Well, they're not physical copies, as they're digital ports on the Wii system, but if that counts:
Galaga - NES - 1981 (although, technically, the NES version wasn't until a few years after 1981)
Super Mario Bros. - NES - 1985
The Legend of Zelda - NES - 1986
Castlevania - NES - 1986
I think those are the oldest, though I do own the early sequels to all these games as well, except for Galaga.
EDIT: Reading through the thread, I see we're talking physical copies... Going by that, excluding ports of older games to recent systems, I think the oldest game I have in possession is ActRaiser (SNES; 1990), Final Fantasy II/IV (SNES - 1991) and Yoshi's Island (SNES; 1995)
I have quite a few NES games stashed away at my dad's house, but I have no idea where they are exactly, so I didn't count them.
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I own Ms. Pac-Man, Bowling, Pitfall, and Missile Command for the Atari 2600, I don't know how old those games are, but they are the oldest games I own.
I'm a sad little panda cuz I got rid of what old collections I did have. If I hadn't the oldest would be Mario Bros./Duck Hunt.. but now the oldest game I have is Bloody Roar: Primal Fury for GC.
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Pinkie Pie's oldest game would be Ghouls and Ghosts for the Sega Genesis, a re-release of Ghosts and Goblins for the NES (she thinks). It was released in 1989.
My brother sold all of our NES games to Gamestop when the N64 came out. (Not only did he have no right, he only got like, 10 or 15 bucks for the console and all of the games. Stupid 12 year old.) Because of this, my oldest games would be my old Gameboy games. I have Metroid II from 1991 and Mario Land from 1989. I think I also have an old 1984 King's Quest floppy somewhere.