I'm gon' lay some cheeezzzzz on this thread.
I was about 8 years old, playing a generic Sonic game on the Sega Megadrive with my dad. We sucked, and we kept dying all the time, but through persistence and sheer luck we managed to finish the entire game, and that was the first moment of gaming which made me feel like pure win.
The only other time I felt that as a kid was playing Metal Gear Solid on the PS1. It was Christmas day when I bossed that badass Metal Gear.
Killing a super-mutant-behemoth with a shishkebab in my boxers on Fallout 3 was pretty epic aswell. For different reasons...