I'm sure I annoy the piss out of some people.
Quake 3's purpose was multiplayer, but Quake revolutionized it. It lead to things such as QuakeSpy (precursor to Gamespy, which was THE server list of choice until they went to suck). The Team Fortress mod was also exceptionally popular. The game was also playable on a 56k modem.
Quake II seemed to be the mass introduction of mods (yes, mods did exist before this, but wowee was there tons of Quake II). One mod in particular was Action Quake 2, which ultimately evolved into Counterstrike for Half-Life. Half-Life decided that stories were not passe, and coupling that with fantastic mod support, it's not too surprising that Half-Life is probably the best selling FPS of all time.
Quake III was out shortly afterwards, focusing solely on multiplayer. I suspect it didn't do as well because Unreal Tournament came out, and offered much more variety in game styles, as well as better bots. The biggest contribution Quake III did was probably it's engine, which was used to create games like Call of Duty and whatnot.