I'm 38, there were quite a couple wow moments in my gaming life however I live in Hungary (a small central european country) and grew up in a relatively small town, I was lucky enough to have access arcades, computers, consoles, so basically everything mainstream. My first one was the Commodore 64 when I was 5ish. We had to smuggle it in from Austria (dark post communist times). It just amaze me that I can control something on the TV screen. Boulder Dash, Pipeline, Mario Bros, I could go on. Then many titles in the arcades, and later the consoles.
Arcade: Contra, King of Dragons, Street Fighter 2, Mortal Kombat, Killer Instinct (especially KI, I remember the first moment I saw it however it was 26 years ago, now I own one original arcade cab)
NES: I mostly skipped it but liked SMB and Contra. I still played C64 and in arcades

SNES: I begged my mom for it with a promise not to go to arcades any more (yeah, I lied). Ok, I visited them less frequently after I got it bundled with Street Fighter 2 and Sim City. Wow moments were Castlevania IV and Killer Instinct, also Star Fox.
PS1: Tomb Raider and Resident Evil. These were the system sellers for me (and wallet killer to my mom

). These two games were absolutely mind blowing back then.
N64: Star Wars: Shadows of the Empire. This made me begging again for my mom, and sell my PS1 (later I begged again to buy another PS1

). SM64 was a blast as well. And Turok (german version with the lame robots and no blood).
Then came the PC in 1997, my first games were Quake, and Carmageddon. I played Duke Nukem and Doom in school before

It was difficult for me at first to aim in full 3D with the mouse in Quake

I skipped the PS2 almost entirelly although I played Colossus and a little bit of GT4 on it. I had Xbox and Gamecube but there were nothing really impactful on these except Project Gotham Racing(X) and Resident Evil 4 (GC). PC remained main platform.
Then came the X360. Became main platform, I bought my first HDReady TV. Gears of War, PGR3, etc. It was bad ass. True next gen feel.
PS3 much later, well after Uncharted released, but it blowed my mind. And The Last of Us.
PS4 came (my first day 1 purchase) Kill Zone Shadow Fall, Resogun, Infamous... The rest is history

PS5, here we come.