I believe it was the Game Boy. I remember my mother saying that, when she was pregnant, she used to play Tetris a lot because you know, can't do silly stuff when there's a little someone floating in your belly. The first console I remember playing, however, was the Megadrive (Genesis for our American friends) with Sonic 2, which, to this day is still my favourite Sonic game.
The one that I remember extensively was a PlayStation, but it might have been a Sega Genesis or something. I specifically remember Panzer Tactics being played, as well as this old dungeon crawler RPG that might be part of the Shining series.
I'll probably have a different answer here, but the first console I played was Nintendo's Family Computer Disk System or in short, the Famicom!
It's basically Japan's version of the NES...I have no idea how or where my parents bought this for me lol
Gameboy if that counts, but probably not. First electronic system I've ever owned with Leafgreen as my first game.
Console though...was the Wii. My parents weren't gamers and so we never had anything video game-y in the house.