Infantry. I learned to type with relatively coherent sentences in short time spans. It also basically ended up teaching me how to spell and was the major cause of me passing most of my middle school english classes.
All of that had absolutely nothing to do with the gameplay or community. The first, well, that was just awesome -- to date, still one of the best top-down multiplayer games (especially re: its engine) I've ever played. Viciously large and chaotic team-based CTF/group combat, with multiple "zones", many of which were games unto themselves -- completely different playing style, graphics, everything. Can't really sum up what my favorite moments, were, though. Most of it can be summed up with 'grenade machinegun', 'grand tank auto X4', and bunkerbusters, which were rockets that shot through walls. Also 'moonwalking through combined enemy forces' fire, stealing their flag, and getting out alive'. That was a good day. Using a tractor beam to drag a tank halfway across the map via mod-spawned UFO was pretty nice, too. Zombie Zone, Combined Arms, Fleet... lot of incredible stuff happened. Even though I still play occasionally via SOE (it's free, and peak still tends to get a few dozen folks), damn Sony to all the hells for nixing what th'FreeInf folks were doing to the engine. LUA support, man, LUA support.
Community was one of the most gleefully self-antagonistic things I've ever had the pleasure of seeing. Think a lot of fairly intelligent people cheerfully tearing each other apart as a matter of course, then ending up on the same team the next round and happily turning on whoever was their former teammates. The raw hate of many of the people playing, and the speed at which that hate would switch targets, was, and still is, oddly soothing. Inf players as a general rule hated everyone not on their team currently, even if they were allies ten seconds ago. A strangle egalitarian and welcoming hatred. "You are one of us," the unending torrent of hate chat said to me, "You phallus-sucking whore monger* good fellow, you."
*Note: Usually said much more crudely.
Anyway, not a single story or anything. My years playing inf as a whole was my best online gaming experience, not any single moment thereof. Lot of great ones, there, but it's a holistic thing, yanno'?