The first game that I ever played was 3D Frog Man on Windows 95, I’m pretty young 
It was either Donkey Kong Land 2 on the Game Boy Pocket, or Tarzan Action game on windows 98
Q-basic’s
Gorilla https://www.youtube.com/watch?v=UDc3ZEKl-Wc&
and
Nibbles https://www.youtube.com/watch?v=fZF6tnrfAX0&t=35s
Either Alex Kidd or Road Rash on the Sega Master System, I didn’t know what I was doing though (I just messed around when my brother wasn’t playing).
Games I actually started playing myself:
G-Police PC
Redline Racer PC
Best of Windows Entertainment Pack (BOWEP)
Got Crash Bandicoot as a christmas present when it was
still full price, best present I’ve ever got to this day (thanks uncle)
^^ All I had for a while when I was a kid was a Tandy PC and that trippy game. I eventually got an NES + Super Mario.
First System, Regular Nintendo back in 1986. First games of that day, Mario/duckhunt combo, Donkey Kong, Tetris and Burger Time.
Either that or tag.
Grand Theft Auto 2. My brother got it when it first came out, he let me play it a few times. I was around 4
EDIT: obviously I played some stupid kids games before, this was my first “real” game
My dad says Putt-Putt: Travels through time
Some atari 2600 game, god knows what it was called, but first game on a PC!? it was on my first, a 486DX33 by Viglen, and the game was Bluesbrothers, at the same time i also had lemmings, wolf 3d, doom and aquanoid. All this in the forsaken ms-dos (although I did later on get Windows 3.1
Peek-a-boo!
But for realz, Road and Track Presents: The Need for Speed
Haha oh shit, I had “Putt-Putt Saves the Zoo,” that game was part of my childhood. We had a lot of the TLC games.
All of the Putt-Putt games were freaking awesome.
I do recall playing a Pajama Sam game at some point- I think it’s the one you build the sock sorter machines for. But I had a Genesis long before I had a computer.
I played the demo for a PS game. It game with Spy Fox IIRC.
That it was.
The earliest game I remember playing was Frogger.
We had a bunch of DOS games on 5 inch floppies. Frogger was one of them.
That would be either Trolls or Raptor: Call of shadows. Both DOS games. Raptor was awesome and it had great music and atmosphere. Beats modern 2D side-scrollers 6-0 easy.
Then I got Playstation and Red Alert on it. Nuff said.
The first game I played was on the PC. This might’ve been a combat flight game whose title I cannot remember, or the original Leisure Suit Larry with the good old parser interface.
This was back in '87 when I was like four years old.
By system:
PC (DOS): unknown combat flight sim / Leisure Suit Larry in the Land of the Lounge Lizards
Game Boy: Super Mario Land
Atari 7800: 32-in-1
NES: Super Mario Bros.
PC (Windows era onwards): SimCity 2000
Sega MegaDrive/Genesis: Sonic The Hedgehog
SNES: The Legend of Zelda: A Link to the Past
PSX (never owned the system myself): Tekken 3
GameBoy Color: PokeMon Yellow
GameBoy Advance: Super Mario World re-release
PS2 (never owned the system myself): Grand Theft Auto III
GameCube (never owned the system myself): Super Smash Brothers Melee
XBox (never owned the system myself): : Halo: Combat Evolved
XBox 360: Dead or Alive 4
PS3 (never owned the system myself): Uncharted: Drake’s Fortune
Nintendo Wii: Super Mario Galaxy
Cant quite remember, it would have been something on the ZX Spectrum
https://en.wikipedia.org/wiki/ZX_Spectrum
However, I pretty much class my AMD386 CPU based computer as the first system I played any games worth remembering. Again, dont know the ‘actual’ first game, but it would have been either :-
Gobliiins
Alone in the Dark (Original)
Prince of Persia
To expand on that further, the ones I really enjoyed the most a couple years later would have been Doom and Worms Reinforcements (had to upgrade to AMD486DX and 16MB of RAM from 8MB to run the cut scenes smoothly in Worms!)
OH and I had to configure DOS Boot disks to bypass windows to gather enough memory to run these things! Even the mouse driver took valuable memory!