The immense joy I felt after finally getting my hands on the N64 and Mario 64 after over a year of waiting.

Also the feeling you would get whenever picking out a new game at the store back in the day, a sense of wonder and mystery at the possibilities of what experience you'll have with this brand new shiny game.  These days with YouTube and "lets plays" you can pretty much experience an entire game without ever actually playing it, but back then all you had to go by when making a decision was the back of the box, and maybe a page or two "sneak peek" in a videogame magazine for new games.

I don't watch those... but the prolonged trailers certainly took some of the thrill... I wouldn't ever be surprised by buying that lot of games with strange names that I knew nothing about.

When I was playing several PS1 games (Driver, Driver 2, Gran Turismo 2) and first experienced Grand Theft Auto III at my cousin's house. I was wowed with what could be possible. I don't think a generation jump like that could be possible anymore.

Playing Ratchet & Clank Going Commando and Uncharted 2 on Christmas mornings of 2003 and 2009 respectively. Nothing will be that exciting on Christmas anymore.

Playing MMOs with your real life friends. Used to do it all the time back in middle and high school and it was great because you had that interaction in and outside the game. Most of my friends don't play games anymore outside of things like FIFA.

Edited the OP. Carry on.

Playing DAOC on the classic servers. The game was fantastic until the release of the third expansion where everything started to go downhill. Recognizing this, the devs released 3 servers that wouldn't be influenced by that third expansion. Then later as the game dropped in popularity they clustered the 3 servers together. Now, they are all part of one server that does indeed take all expansions into account. So never again will I get to play an official classic DAOC server.

Playing through mgs3.
Or when I realized all the characters in journey were other players.
Or playing the Last of Us for the first time and just being blown away.
Going on my first null-sec raid in EvE with like 400 ships battling each other in 3d space. Shit was so epic.

Going to my local arcade and kicking all kinds of ass in Street Fighter or Killer Instinct. I used to have a crowd around me (or maybe they were just waiting for their turn). I felt like a star!

When Edge realized that things aren't as black and white as he thought, I got a true chill down my spine and it suddenly made the game even greater (Panzer Dragoon Saga). Also, first time playing Pitfall 2 and feel like I was like Indiana Jones in a video game was a magical feeling.

Playing Secret of Mana local coop with my 2 brothers on SNES w/ Multitap.

We were young and lived together so it worked but now we're all grown-up, moved out, relationship, kids etc.

THE best couch coop I've experienced. Being the 3rd and youngest kid multiplayer games that were +3 players were rare back then so I've always more so was left out as most games were 2 player coop at best and my 2 older brothers would play/hog it.

I'm glad one of my earliest and best experience playing a +3 player coop game was also a fantastic game.