NES: Super Mario Bros.
First game I probably actually played.
PSX: Final Fantasy VIII
The most defining game in my youth. A perpetual favorite of mine. Will always hold the "nostalgic #1 game" spot for me.
PS2: Final Fantasy X
I bought the bundle with FFX in it, so this was the first game I played on the system. Gorgeous game, excellent story, lovable characters, amazing soundtrack, an all around fantastic JRPG experience.
PS3: Final Fantasy XIII
I stepped out of console gaming during this generation so I actually played a little amount of games on this platform. FFXIII however will always hold a special place because this was the game I spent my entire summer holiday on before heading of to college. I finished it like a week before the academic year started, and I strongly associate it with the end of a large chapter in my life, namely high school. I love it and I'm so glad I get to finish its series on the PC now, funnily enough when I'm 3 semesters away from graduating.
PC: DOOM
I have special memories of this game of me and my sister deathmatching and playing coop. My sister has grown out of video games a long long time ago, unfortunately, but connecting LAN cables and just figuring out the maps in DOOM 2 is a very vivid memory of mine.