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?
Xenon 2: Megablast on 5½" floppy on my mum's work-issued MS-DOS PC (featuring a monochrome orange & black monitor). We also had a flight simulator and a golf game, iirc, but it was Xenon that left its mark.
We later got a cheap NES (this was after the SNES had been released, so they came into our price range) with the Super Mario & Duck Hunt double feature cartridge. That bright orange light gun made me feel like I was in the future.