BSOD
RROD
YLOD
BEEP
GAME OVER

You can put text in black to prevent spoilers. 

5) Getting an Intelavition back that n the early 80's. Was better than the Atari. I still remember playing Tron Deadly Disk.

4) Dune on the NES. Was the first RTS I remember loving loving the concept. Still love it today as RTS' s are my favorite type of game. Can't wait for 3rd installment of Star Craft 2.

3)Out Of This World. I like the first better. Don't know if there's been others games with the same concept, but would love to see a third part with current tech.

2) The first Legend Of Zelda on the NES. Totally fell in love with that game and Zelda is still my favorite series today.
Was disappointed that Zelda Wii U was pushed back to 2016 but better to wait for a better game.

1) Mario 64. Still my most fondest memory in gaming for me. I don't think it can ever be topped.

I organised my moments by franchises.

5 Pulling out the master sword in twighlight princess after a lovely Temple.

4 Playing F zero GX for the first time

3 Killing every boss in Bloodborne without help in a single playthrough.

2 The train sequence in Uncharted 2 or Boat in Uncharted 3 or Planet sequence in Uncharted 3. Something Uncharted like at least.

1 The first bossfight in God of War III or killing Chronos.

Honourable mentions
Destroying the stuff on the space needle in Infamous The last of us,

The graphics of either the order or Driveclub,

Titties and the deheading scene at the beginning in the Witcher 3.

Entering the world of bioshock so beatifull with the whale and a giant squid.

Captain Qwark's jokes and the humor in Ratchet and Clank (looking forward to the movie)

I picked Infinite's plot twist but the elevator ride in the first BIoshock would have easily taken that spot had I played Bioshock when it came out in 2007.

I remember that tv trailer they had with the music... oh the feels.

I played the second one first, but that moment was awesome, so that's why it is a Honourable mention yet the list would not be complete without it. I am surprised I am the first one to mention God of War 3. Another moment I can think off that deserved the list was killing my first dragon in dragon age inquisition with minimal level requirement and the plot twist.

I love this thread idea. Let's see what I can come up with.

When you first land on Tallon IV in Metroid Prime.
https://youtu.be/dRjgQGW0_DQ?t=8s

The opening of Super Mario 64 where you can stretch out his face.
https://youtu.be/stK4h115y70

The beginning of Super Mario 64 where you see the castle in all its 3D glory and get to run around the court yard.
https://youtu.be/KN7o97fwCNg?t=1m15s

Meeting and entering The Great Deku Tree in Ocarina of Time.
https://youtu.be/1liH6CrZ-sg?t=1m10s

Getting Epona for the first time in Ocarina of Time.
https://youtu.be/PHuoWnOoBTo

There are probably a bunch of others, but that is what I can think of for now.

Terranigma: ending
resident evil 4: chainsaw man!!
Super mario kart: time trial on mario circuit 1
Gta 3 vice city: Billy jean

Mine are going to sound nooby, but:

5.) Outlast - When Walrider shows up in the dark courtyard level.
4.) The Last of Us - the beginning climactic scene when they're escaping the city.
3.) Rain - pretty much the entire game. I love Claire de Lune. lol
2.) Illusion of Gaia: The ending when Will and Kara fly to the new world.
1.) Metroid Prime - Stepping out onto Tallon IV in the rain for the first time and hearing that epic, anthemic Brinstar theme in the background.

And pretty much a million moments from every Zelda game. Too many to list there. Goosebump moments are the best!

Oh, also first setting foot in the Underwater Frigate in MP and hearing the best theme of that game legit gave me goosebumps.