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?
My first experience was with my cousin who had the wood grain Atari 2600 which blew my mind. He even opened up a cartridge for me to show that it was all electronics inside. I thought there was some kind of film reel inside but couldn't figure out how that would work.
Not long after, for Christmas, my parents got me a ZX81, but it was in a beautiful custom wooden case (it's not this case, but that is the keyboard that was used. I remember those two red LEDs as well for CAPS lock and Symbol Shift lock). It also had the 16k ram pack which was soldered on, all inside the case. There was no worries about wobbles and crashes.
I wish I still had it, my father was a carpenter, so I'm sure he made it. The top was matte black, and it said ZX81 + 16K stencilled into the top in bright red.
And so my love of computers and gaming was born.