While Quake II and III are arguably better games than the original, they couldn't match its impact. Quake changed the world and the industry, and its legacy is as big as Super Mario Bros., Space Invaders, Pac-Man, Ultima, or even Doom. It influenced more areas of the industry than any game before or since: coding, level design, online play, modding, computer hardware. Quake's influence is still felt today long after its particular take on the first-person shooter has fallen by the wayside.
cutscenes are now content. story is no longer just context in games
i see this as the major problem in modern game development philosophy and hardly any designers are actually acknowledging it, probably because they are blinded by the money
i guess it's not really a problem to them if they're making money, but it's a problem for people like us who actually care about the game
Well, the upcoming Modern Warfare 3 uses the continually updated Infinity Ward engine, which bases it`s roots in id tech 3. (Original COD used id tech 3 before IW was in development)
But that is really about the extent of it. Most of the "influence" is more engine-related than story or gameplay-related.