I think the most memorable encounter I have played in would be part of Lowell's World of Darkness game. We were on the track of an informant and our Assamite player did not catch on to something the rest of us caught in an interaction with the Prince or some other higher than us in station muckety muck. We broke into the informant's apartment and discovered vampires can't see in the dark without flashlights - or at least our vampire assassin couldn't. We crept into the bedroom and the Assamite did what they do best, he killed a human informant by staking him through the heart!
You see, the player had it in his head that this NPC was a vampire that needed staking. We broke for a smoke break, came back in and replayed it.
But there's always the first year we ran demo games of Buffy the Vampire Slayer and the high number of women who came out to play for the first time.
And running an one shot of Night's Black Agents and thinking, this is a damn cool game.
And discovering that World of Darkness first edition and early second edition combat rules were bad for Werewolves. I could hit a gnat, but could not do more than one point of damage on TWELVE dice.