Tons of Nintendo memories.  Top 5 are probably:

-First time I played the NES / SMB at my grandparents' house Christmas '87

-Getting the SNES & Super Mario World shortly after launch.

-Getting Donkey Kong Country for my bday.

-First time ever playing the N64 / Mario 64 demo kiosk at Toys R Us before the system launched.

-Alternating between MK64 and SSB tournaments with my roomies at college.

The first time I got a Nintendo DS, which was also my first console ever owned. My parents were poor but some eastern guy managed to sold us one thanks to me insisting on it over and over and over again like a spoiled child, and the support of my godfather who was visiting us at that moment. 

It came with the Revenge of the Sith game, which was good enough for me. Beat that game plenty of times, then I obsessively kept coming back to the console, even if it was just doing random Pictochat drawings. Fun times, those. Life were much more simple.

I also love how in high school, a bunch of us brought our DS and play Mario Kart. And I like how we had to stay close together when we moved from one class to another.

And basically everytime I brought my Wii U to School and played them party games like NintendoLand , MP10, Wii Party U, MK8.

The first time i played super mario brothers and mario kart were my fondest memories

I remember when I first completed the Pit of 100 Trials in Paper Mario TTYD. I was so damn happy!

255 million systems sold last gen.

Also: Wave Race Blue Storm (my very first console game), Metroid Prime, A Link to the Past and Paper Mario TTYD.

The opening cutscene of Metroid Prime probably stands out as the most memorable shot of gaming to me.

Getting a GameCube and being able to play multiplayer Melee

Was my first home console that was great

I have a few great Nintendo memories:
1. Finishing Super Mario Bros.
2. Teenage Mutant Ninja Turtles 2 co-op play was a big deal.
3. Finishing Castlevania III the first time.
4. Getting Mario 3, my first hugely anticipated game.
5. Gameboy! Me and my sister got one each at Christmas, that was a big deal.
6. Getting Nintendo 64
7. Playing GE007 with friends for about 30+ hours in a row, and the nightmares that followed, as I couldn't dream correctly for days after.
8. Turning on Ocarina of Time for the very first time, and letting the intro play to my most anticipated game since Mario 3.
9. Wii Mania, standing out in line with dozens of others waiting for the store to open, about 17 times.

Unfortunately, not many things have stood that strongly since Wii Mania. I think the biggest one was seeing the Xenoblade Chronicles X trailer where they showed Gears, I was a gigantic Xenogears fan, but playing it I was a little disappointed that it didn't tie strongly into Xenogears, but the opportunity to explore a link is still there!

late 90s-early 00s

pokemon was exciting both on tv and gameboy
playing snes and n64 at friends house while they came to me to play ps1
summer days playing tony hawk underground, wind waker and mario sunshine

man those days had magic