Well erm... Where to begin, honestly.
So many games, so many moments - I'll just list a few of my favourite moments that I can vaguely remember, but it's like trying to remember every good book you've read...
Way back in Diablo 2, just anything I did with my Blizzsorc was awesome, every duel game was just a chance to show off.
In command and conquer generals, taking on my brothers, my friends, and some randoms by myself, and winning. Thrice.
Pretty much same goes for SupCom2, RA3, some other RTSs.
In WoW (yeh, I've quit now, don't judge me), realising that main was enough time to restealth in for a druid, and the same with cyclone: before the patch, I was one of the few players who had the restealthing stunlock down to a T, resulting in flawless 1on1 victories.
Also when I played against a mate of mine, as a lvl 65 hunter, where he was lvl 70 epic geared, my survival/marksmanship spec focused on continually stunning and aimed shot critting landed me loads of easy PvP wins, again before they patched aimed shot to an instant cast... Bastards...
In Air Rivals, My Igear could (can, I suppose) fly faster than the missiles it shot, so on a long attack run my favourite thing to do would be to stack missiles travelling next to each other, and then when I flew over the enemy they went "huh?", then exploded.
In Global Agenda, with my recon, someone tried to backstab me while I was sniping, I jetpack off, turn while flying and snipe them, even if they're stealthed. Happened a number of times, I can almost feel their 'wtf?'.
And in DotA/League of Legends, every game was essentially this: it's my main competitive genre, and I'm so far unmatched at it. This sounds essentially like a massive boast, but if you're any good, I'd love to play you, the matchmaker is shocking.
Ah... Good times...