I'm aging myself here.
The first game I really played (aside from my granddads super old Pong console) was Sonic the Hedgehog on my Sega Master System II.
Don't remember much of it, but I know this: I never played a Sonic game since. I guess it just wasn't for me.
What about you?
I think the first one for me was probably Donkey Kong country on Gameboy, I just remember the car rides at night where you could only play when the street lights shone through the window