Two that really stick with me:
Grand Theft Auto IV: Stalking my unwitting friend in a helicopter in Free Mode, scaring the crap out of him by shooting up his car and chasing him around for a good 20 minutes.
His face when I told him it was me the next day was fucking priceless.
Oblivion: A glitch counts as one of my all time favourite gaming moments:
In the early game, on the way to or past Kvatch (don't remember which), I stumbled across the ancient ruins of Miscarand. It looked too interesting to not look in, so I sneaked past the goblins on watch outside and delved in.
The place was monolithic and not a little imposing for my first proper attempt at a dungeon. Thinking about the potentially awesome loot, I steeled myself for the journey ahead, creeping through level after level, carefully avoiding death traps, skeletons and headless zombies (enemies that were very tough at my low level).
A couple of hours later, I reached a large antechamber. At its centre, a glowing white crystal. I hadn't seen anything like it in the game so far and, Raiders of the Lost Ark vibes aside, I knew I wanted it.
I should've listened to Indy.
As soon as I had lifted the crystal from its plinth, a section of the wall behind me cracked open. I turned. From the darkness, a terrifying apparition slowly emerged; a magnificent floating corpse crackling with magical energy and humming with the malevolence of Hypno-Toad. It was, I would later to discover, a Lich-King. Not just any Lich-King either, it was a named character: The King of Miscarand. Not gonna lie, I shat myself. Before I could apologise for intruding, he seared me to within an inch of my life with one bolt of electricity. I ducked immediately behind a pillar and carefully weighed up my situation, concluding that all I had that could benefit me in this fight was my preternatural speed.
So I fucking ran.
I ain't too proud to admit it, either. I ran straight out of the antechamber, through each of Miscarand's levels, narrowly dodging all the monstrosities I had carefully picked my way around on the way in. It had taken me the better part of a couple of hours to work my way down there, it took a few minutes to escape. Once in the daylight and out of sight of the Goblins on watch, I carried on running. I never once looked back.
A few weeks in real time later, I was visiting the Duchess (I think) in Burma. By now, I was a full fledged member of the Theives Guild, acting as the Right Hand of the Grey Fox. I was hob-nobbing with some of Cyrodil's most influential people. I was confident in my abilities, as well as my understanding of the game and its mechanics. Few obstacles couldn't be solved by guile, a bow or a sneaky knife in the back. I was practically an elite ninja at this point.
I stepped out of the keep and into the courtyard. I heard the sound of nearby battle. This seemed odd considering I was in a city. As I went to investigate, the corpse of a guard fell from the sky. What the fuck was going on? When I turned the corner, I found out: The King of Miscarand had followed me across Cyrodil and into Burma. He was now murdering guards, civilians and merchants alike to get to me. He'd even brought a couple of headless zombies for company.
He really wanted his crystal back.
The image of the Lich-King hovering slowly across the Cyrodil landscape - cursing and muttering under his breath, Hypno-Toad buzz ebbing and flowing with his emotional state - is a potent one for me. It was my first 'Next Gen' moment. This videogame character had 'remembered' my little indiscretion from dozens of hours ago and, completely unscripted, chased me across the map to settle the score.
The whole thing blew my mind.