EPIC moment:
Double Dribble - knowing that spot for the 3point shot. Imba
Diablo I - that cheap to duplicate items... massive.
Diable II - going to PC rentals and getting all those items from other players.. lol
Counterstrike - killing enemies with knife only
Super Mario 3 - those flutes. and borrowed a Super Mario 3 with cheat (all items using select button) and my goal was getting each 1 up (or sometimes more than 1 green mushroom) per stage. :D
Final Fantasy XIII-2 - defeating Caius (2nd Caius fight) and i didn't grind that much so it is really a hard battle.
Fifa 14 - platinum trophy
NBA Live 2004 - those mods to use local leagues.
Dota 1 - Friday night dota with officemates. until 3am on saturday... then have football (soccer) intercompany games on saturday 10am. :D
Dota 1 and 2 - God like.....
Fighting games and NBA Live on PC - we don't have controllers at that time, so keyboard and it is shared, my brother uses the qwerty layout. i'm using the nearly impossible numeric and arrow buttons on the right.... and elbowing each other to get the advantage....

this is my list for now. ;)

Hmmm.
1) Beating the Vault of Glass with my Crew for the first time (Destiny).
2) Beating Yiazmat in FF12
3) God of War 3 Intro
4) Uncharted 3 plane sequence
5) Getting big boss emblem in MGS 4

A newest one that happened me was playing Witcher 3.

Was killing some cows when I saw all the towns people screaming and running away. I figured it was because I just killed their cows. So I was like "Don't worry I'm just going to kill your cows." Then I notice a shadow next to be so I look behind me to find a giant beast, All I could say "Oh shit!" before he killed me in one hit. :P

I beat Virtua Fighter on hard mode in 1997, surpassing my older brother and all his friends in video games despite being 3 years younger than them. This is coincidentally around the same time my older brother last interest in video games. 

I beat Panzer Dragoon Zwei, being the first game with a recognizable sorry that I beat on my own. 

I beat Sephiroth at level 38 in Kingdom Hearts, a feat which necessitates not getting hIt ONCE. 

While demonstrating Monster Hunter (PS2) to a friend, I felled a Rathalos and a Rathian in the same sword swing. I was being pincered by them, and I swing up and backwards with my Greatsword. Contact with Rathalos face on the upwards motion (dead), slammed down into Rathian face on the way down (dead, too).

Killed an entire eight-man team at the same time during a game cage LAN of Halo 1. Sidewinder, capture the flag. The other team has a warthog in their base in front of the flag. They also have noob cannons. I hop in my warthog, drive in their base, and swish them all against the wall by taking their warthog. The entire building lights up with laughter as I grab the flag and deuce out. 

I found a PS3 in my mom's closet in late November '06 and literally shit my pants. 

Built my first gaming PC.

Fried my first gaming PC. 

First gaming ending that made me clap: inFAMOUS. Kessler's identity was keep so vague until the end that it was genuinely surprising who he was, and it makes sense in the second play through while never feeling like "Oh, I should have picked up on that".

I Platinum'd my first game: inFAMOUS. I Platinum'd inFAMOUS 2 shortly after. 

I paid for my first gaming console (previous consoles all being presents) in the PS4. 

I Platinum'd Bloodborne, Scholar of the First Sin, and Demon's Souls back to back to back (aka, I got gud).

Built my first gaming PC since 2007.

The day I got Shenmue. Never before was I totally absorbed into a video-game like this. More than 15 years later, I have been living in Japan for 12 years. I didn't realize yet at the time just how much this game would influence the rest of my live.

Wow, that makes me really want to play The Witcher!