Mine was Snipes, a 2 colour DOS game that came with Novell Netware - http://www.textmodegames.com/download/snipes.html
In my first job at lunchtimes about 6 of us used to play this game.
It looked crap and had no sound, but it was the first time I had ever played a multiplayer game with more than 2 players -apart from Lotus with 2 split-screens, and a bit of KO/Sensi/Bomberman. Obviously the fact that it was a maze-style shooting game and it was important to have your own monitor for yourseld (no split-screening) it easily beat the Amiga in terms of multiplayer fun.
Then of course along came Doom.....