If electronic games is implied, I started with bomberjack, Joust, and the likes. Some "not so orignial" consoles came with preinstalled games. Hence.
Someone played the original Castle Wolfenstein? wonderful! I spent days? no, weeks or months on that simple game.
Duk hunt, at least that's the one I remember. Dig dug, Mario, Street Fighter etc. They are all a mash in my memories because they were played so close to one another. I do remember the first game for each of my consoles though.
I got a Nintendo system for Christmas when I was six years old and it came with Super Mario Bros. I didn't get any sleep for a very long time after that.
Besides Super Mario and Donkey Kong on the Super Nintendo - the first game I really played through was Zelda: A Link to the Past, and then Ocarina of Time when the N64 came out. Oh yeah, those were the days!
Super Mario Brothers 3 on the Nintendo console my dad bought for us from India. Gosh, it was state of the art and amazing at that time.