My first online experience was in FS3. Dial up modem, direct pc to pc connection, 1988.
I was at home, my friend in his father's practice (family doctor). Ofcourse while connected we couldn't communicate. Yet it was still magical to see that other plane in the sky and follow each other around.
I had lots of great moments in Duke Nukem 3D played in the office lan. There was a map where you could hide underwater (not transparent at the time) and try to hit someone coming along based on sound, which promted them to start shooting rockets into the water and throwing pipe bombs. Very hectic game of predicting where the other person thought you were.
It also had a level with an elevator to the top of the building with a few good power ups. Yet the call button at the bottom always directly reversed the elevator back down. The battles for the elevator were pure awesomeness. Trip wires, trying to hide in a corner in the elevator, chugging a pipe bom in it, rush out with a shotgun, send a rocket in as the doors open. So many possibilities.
Online multiplayer never managed to get close to all the lan fun we had with Duke Nukem 3D, Half-Life, Quake and Unreal Tournament.
My best oline gaming moments are from Everquest and some from WoW.
Well, once in Journey I met another player that was as interested in pushing the limits of the game as I was. While chain boosting each others flight we managed to get deep behind the scenery to explore areas you're not supposed to be. That was pretty special. Never knew who it was.