Oooh... Let's see...
We started out playing River Raid on the Atari. This and missile command was the only game I remember, but I'm sure there were more, as we were swapping cartridges with our neighbor.
My dad came back from Japan and got us a Family Computer. After a while, it was replaced with a NES. Or whatever the hell it is, because when I search for NES, it doesn't look like our NES. But whatever. It plays the bootleg cartridges we bought. Tons of them. This included, of course, Mario 3, one of the best games ever.
I was sick one day, and I wanted to play GI Joe on the NES, so I asked my mom for permission. She said no, but said go play on the computer (PC). I didn't realize there could be other games on the PC (I thought the PC was for work and the only game on it was some sort of typing tutor). We played Steel Thunder (the most awesome tank sim ever!), Dune 2, and the 2 Prince of Persia games.
My dad got us a SEGA Megadrive (16 bit!), and there was Sonic, and Royal Rumble (we were crazy about the WWE back then). I got my mind blown by the X-Men game. At the end of one level, Professor X asked us to "reset the computer now!". There were no switches anywhere. Could he talking about the reset button on the system? We pressed it and woah... mind blown.
Then my dad came home 1 day and got us Eye of the Beholder 3, for the PC. This was awesome. It was our first RPG, and it got us into RPGs, and I only stopped playing RPGs when I bought my first ever console, which would come later.
In any case, we played all the D&D games. EoB 3 (we never had 1 and 2), we then got Ravenloft, and Menzoberranzan (Drizzt is awesome).
Dad bought TES: Arena, but during the intro there was this error: "Memory list blown.". So we never got to play it. Not sure what the hell that was, I guess we didn't meet the system requirements. We went back to our D&D RPGs. Then he bought TES: Daggerfall (seriously, I don't know where he gets these games), that game made us upgrade our hardware due to its whopping 200 MB of required disk space. I love this game. We played this for about 2 years non-stop, almost never playing anything else. Just the sheer size of that world and all the things you could do in it. This is probably my all time favorite game.
This led to Fallout, then Fallout 2, the Might and Magic RPGs, then TES: Morrowind, Baldur's Gate, Icewind Dale and Neverwinter Nights, and other RPGs in between like Arcanum and Lionheart. I loved western RPGs. I was a PC gamer race all the way up to college.
Then I got a job. All this time though I had really wanted a PlayStation. I never had a PS1 but I've played some on my friend's house. So anyway, around this time, FFXII was released, and I bought a PS2 as recommended by a friend. This was my first jRPG ever, and I loved it. I had thought the genre was silly, due to it's little boy protagonists compared to the grown men adventurers used in Western RPGs. Anyhoo, This got me into other jrpgs like Chrono Cross (which I played on a hacked PSP), and FFX. I thought both these games had an amazing story, I loved the twist in Chrono Cross, and I loved the drama in FFX.
Later on, I got a PS3 because I wanted to play TES: Oblivion. Crazy reason, but that's what it was.
Then I got an XBox 360, mainly because of Mass Effect and Lost Odyssey.
And recently, I got a PS4. Still have to find a defining game for the system.