The ones that stick out for me are-
Playing in a MLG and getting to meet a bunch of my favorite players (Grubby / Nony / Jaedong / Demuslim / ect). Tons of cool stories from this, but probably my favorite was winning a game and hearing people calling my name afterwards.
Staying up till 5am with a friend drinking beer watching the GSL finals just a few days after I turned 21. It was the Soulkey vs Innovation finals, and I bet him that Soulkey would win. I ended up being right, but I thought it would be on the back of epic macro games, not Inno choking though.
Beating FFVIII for the first time- this was my first big JRPG I beat and I played the game a bunch before I had a memory card so I had to restart from the beginning every time. When I finally got the memory card and got the see the rest of the story, it was pretty awesome, even if I had no idea what was going on in like half the story.
Playing Brothers: A Tale of Two Sons. I played this with my girlfriend watching, she really enjoyed the game just for the aesthetics / puzzles, but at the end I started crying at what to her seemed like a really random time and it's impossible to explain exactly how the mechanics of that game worked so beautifully without playing it yourself.
The infamous fishing village mission in the original XCom. I went into this mission blind but playing super safe, and still lost 2 soldiers. I would have lost 4, but I decided to take a risk and have the 2 who were going to get out safely turn around and keep fighting to try to get the others out. I had a Gernadier who I realized wasn't going to make it out, so I had him move forward slightly to draw the aggro and get surrounded then blow himself up to kill off a decent number of the Cryssalids. So many epic mini stories happened in mission, I was literally bouncing in my seat.
Playing the Warcraft 3 campaign for the first time and getting to the part where Arthas burns his men's ships. We had just been studying the Spanish conquest of Aztec Empire in school and specifically Cortez burning his men's ships, and this historically accurate tie-in with Arthas' actions made the experience that much more awesome for me.
I could probably list quite a few more if I really wanted, but these are the ones that came to mind immediately.