-Atari 2600: the first time I put my hands on that controller and played Yar's Revenge (my very first gaming experience that I can remember.
-NES: Playing Super Mario Bros. for the very first time at a Sears kiosk and not understanding the controls! I kept running into the first goomba, and then I figured out that "A" made Mario jump (I was five!). My mind was blown!
-SNES: Final Fantasy III (VI): The "end of the world" scene where Kefka puts the statues together.
-PS1: Playing Battle Arena Toshinden (yuck!) and thinking to myself: "I have Virtua Fighter......in my living room!"
-Gamecube: Metroid Prime. 3D Metroid, in first-person mode! And it worked!
-PS3: Uncharted 2. The opening sequence where you wake up in a train that is hanging over a cliff.
-PS4: Dark Souls III: The excitement of FINALLY beating the King of Storms/Nameless King!

3rd - Playing Final Fantasy for the first time. Up to that point I had only played Mario games.

4th - Final Fantasy VI. Kefka's actions on the floating continent. Actually made me reset the game the first time because I thought I did something wrong.

5th - The motorcycle portion of the FFVII FMVs.

6th - Xbox. No game in particular. Just the idea that someone else could enter the market at that point and find success in a Ninty/Sony world.

7th - The world and story of Bioshock

8th (to this point) - Feeling like Spider-Man

I've been gaming since 2nd gen, but have only been "Wow'ed" a handful of times, and almost always by graphics advancements.

3rd gen - seeing games on the NES that I had previously only seen in arcades, like Excitebike, Punch Out! and Super Mario Bros. Also, as others have mentioned, seeing epic scale games like Legend of Zelda and Final Fantasy completely changed what I saw games could do. While I enjoyed many, many games for the next decade on consoles and PCs, every advancement after that seemed iterative to me until:
1997 - My first graphics accelerator. I got a 3dfx Voodoo card, and seeing Quake and Doom and racing games run with soooo much better graphics AND higher framerate was just amazing. The next wow moment came much sooner:
1998 - Half-life. Just the way the game progressed with in-engine cut scenes and how the military units were actually intelligent in how they attacked you was pretty mind-blowing. Then, a couple years later:
6th gen - Seeing Madden 2001 on the PS2 for the first time running on a Best Buy display (where I worked at the time). This was the first edition of the game that had close-ups of the players between plays, and it was a massive step up graphically from the previous gen versions of the game.

Since then, I don't feel I've been wow'ed by anything, really. I kinda fell away from gaming as my career and family took precedence until my kids were old enough to game and I got a Wii late in its life, and now a Switch. I've liked both and also have continued PC gaming but don't feel I've been wowed in a while. The advancements seem so much more subtle now.

Gen 6: The opening level of Rogue Leader. On a CRTV it really looked better than A New Hope.

Gen 7. The first time playing Wii Sports. Motion controls have been my preferred control method ever since. Prime 3 for the revelation of its pointer controls. Gears of War was mind-boggling in 2006.

Gen 8. The first time I saw the 3D effect on the 3DS. Sometimes I still feel like glasses-free 3D is technology from the future even if the novelty has worn off. Playing games like Breath of the Wild and Mario Odyssey on the go. I may prefer to play them on a TV, but having games that big and beautiful in my pocket is a wonder.

Atari- Pitfall 2 (that open world!)

NES- Super Mario...or maybe ROB...or maybe Zelda, but really...Metroid. Metroid had the most lasting "wow" feeling. ROB's was the shortest. Super Mario was actually in an arcade cabinet, so I'm not sure it counts. And Zelda is definitely up there with its gold cartridge and expansive world.

Super NES...Super Metroid. There's just no contest here. I loved Super Mario World, but it didn't truly "wow" me. Secret of Mana was probably also a high mark of "wowness" for me, mostly in that I had never heard of it and I was being shown all of these cool action RPGs at the time, including Illusion of Gaia and Secret of Evermore.

PS1/N64...Final Fantasy 7/Mario 64/Zelda: Ocarina of Time...this generation was probably the most "wow" inducing of all time for me. Each of those titles had me grinning ear to ear playing the whole time and just being dumfounded at the potential for videogames.

PS2/Gamecube...Smuggler's Run (crazy open world, go wherever you want)/Metroid Prime...Metroid Prime was stunning in its expansiveness, the incredible graphics, and just the thought that they turned Metroid into a First Person Shooter (adventure) and I was loving it so much. This title single handedly brought me back into the Nintendo fold.

Wii...WiiSports...nothing gets a bigger wow for me than this title probably, and that includes Mario 64, Zelda Ocarina of Time, and Metroid Prime. The motion controlled game just excited me so much about the potential of the Wii that I almost couldn't contain myself. Of course, the waggle lovefest was short lived, but for the first couple months of playing WiiSports I was enthralled.

WiiU...Mario Maker...wow, you can make all these levels?! I thought it was the nail in the coffin for 2D Mario, and as of this writing they haven't made another 2D Mario. Only time will tell. Also, Lego City Undercover and its beautiful use of the Gamepad. I could finally play one of these open world car stealing games without the guilt of GTA.

Switch...Breath of the Wild, and the moment you walk out of the Cave of Resurrection. The "wow" factor doesn't ever fade, either. Here's to hoping its sequel can achieve the same thing.

PS1 Gran turismo 2. The cars looked super "realistic"'.
PS2 FFX. The opening cinematic with blitzball and Sin blew me away and the music was kickass.
PS3 Demon's Souls opened the door to my favorite gaming genre.
PS4 Bloodborne DLC old hunters, Greatest 20 dollars I have ever spent. The music, the boss fights, the atmosphere. Bloodborne in general is just on another level.

As I primarily game on PC the gens get a bit blurred for me, but the moments that stick out:

SNES: Super Mario World- I'd never played a platformer that controlled so smoothly
PC: Doom- First time playing a first-person 3D game was mind-blowing
GB: Zelda: Link's Awakening- The realisation that they'd managed to cram such a huge game world into a hand-held.

PS1: FFVII- The opening of FFVII and the narrative thread that ran through all of Midgar made me realise the storytelling potential of games.
PC: Half-Life- The opening again completely changed the way storytelling in FPS' worked whilst the AI actually seemed believable, especially for the time.

PS2: Metal Gear Solid 3- The ending was an emotional roller-coaster
PC: Deus Ex- Realising the sheer number of ways I could complete each level and complete tasks in hub areas.

PS3: Uncharted 2- The level with the helicopter and the collapsing building whilst fighting. First time in a game I'd experienced anything like it.
PC: Oblivion- Not sure when but at some point during my main playthrough I just felt like I could find myself living in Cyrodil
Mass Effect 2- The suicide mission and the way the whole game inter-weaved and lead up to that point

PS4: Uncharted 4- the ending was perfect
PC- Witcher 3- Just... everything. Completely raised the bar for wRPGs.

Dude.  Seriously.  The first Unreal was next level shit. I mean, I guess Doom and Quake were both next level for their time as well.  But Unreal was jaw-dropping.

Monster Voodoo 1 here.

Gen 2: Vector Display Screen.

A retrospective entry as I only experienced the Vectrex later on in life. Images simply don’t do this justice; the screen is like heroin for the eyes. You simply have to experience the crisp glowing lines for yourself.

Gen 3: Bootleg NES Multicart.

The holy grail. My tiny mind couldn’t comprehend this 999-in-1 cart with every game at my disposal.

Gen 4: Street Fighter II Arcade.

These bad boys were everywhere and everyone was either already playing or stepping up to challenge you. Gaming was cool and the arcade version crapped all over any console fighter that came before it.

Gen 5: Four-Player Pandemonium.

The N64 upped the local multiplayer game to 4 frenemies, with a plethora of quality titles. Racing, fighting, stupid mini games - it had them all.

Gen 6: The Internet Finally Works.

Battlefield 1942 was beyond epic in scale. You weren’t a superhuman commando snowflake but a basic infantry unit thrown in with 100 just like you. Everyone’s weapons sucked and everyone died easily. This was a grand war and only the internet could make it happen.

Gen 7: First Time Holding the Wiimote.

Sure it seems so basic now, but at the time that cursor following your movement, rotating as you twist your wrist and rumble feedback as the cursor passed over menu icons was incredibly immersive in its own right.

Gen 8: Asymmetrical Gameplay.

Nintendoland and some earlier WiiU titles showcased the joy of asymmetrical gameplay. Luigi’s Ghost Mansion gives one player more information and more power than the rest for a 1v4 showdown which felt nicely balanced for a tense game through to the end.

Gen 9: Reliving the Glory Days.

Snappy as all hell, the Switch turns on when you press the power button. It loads games when you select them. Fast.
This is what cartridge gaming was all about and the Switch reminds us just how far we’ve strayed.
Breath of the wild also takes the Zelda series back to its roots for the first proper modern open world experience. I felt a true adventurer with the complete freedom given.

Gen 4: Civilization (PC)
Gen 5: Oot (N64)
Gen 6: Everquest (PC)
Gen 7: GT5 online racing
Gen 8: PSVR