Quake 2! I know they tried with the single player in Quake 4, but the online community for Quake 2 in the 90s was the best community I've ever been a part of (haha, no offense guys....but we can't exactly play each other). Maybe the fps genre is too over saturated now for that large of a community to stay active for so long to ever be possible again, but I get a warm, fuzzy feeling when I think about Quake 2 CTF and the social community (haha, anybody who was anybody had ICQ and mIRC by '98/'99 to communicate with their clan). I loved playing online and the huge lack spikes, 400+ ping on some servers, and everything else that comes with playing online with 28.8k dial-up modem was easily overlooked cause I didn't know any other alternative.
What made gaming communities so strong back then was that there weren't tons of alternative games to play with the same features and there weren't different mediums to play the games on dividing the community. You couldn't connect to the internet with a console (iirc Dreamcast was the first one, but it wasn't released outside of Japan until almost 2000, and even then not many people played it for its online capability) so if you wanted to play a game online, pc was the way to go. Just think about how absurdly huge some communities would be today if everyone played online on the same device and if sequels and copy cats weren't constantly churned out in yearly intervals to make a quick buck and totally divide the community even further.
So maybe it's nostalgia, maybe it wouldn't matter if the game was remade :/
I would say Quake 3 also, but they struck such a delicate, almost perfect balance in the competitive scene that I'm not sure if it's possible to be improved upon. It would more than likely be messed up and I'm satisfied with Quake Live.