Master Crimzon
Baby Killer
Rating the most influential (NOT my personal favorite or even close to it, for that matter):
Sci-Fi: 2001: A Space Odyssey for the intellectual, cerebral sort of science fiction and Star Wars for creating the the 'special effects popcorn film'. As to who actually had a greater impact upon the genre... well, I'm going to have to go with Star Wars here. Tough call, though.
Action/Adventure: I'm going to have to go with Die Hard here, too. It pretty much is the template for the modern action picture.
Film Noir: I honestly don't know, being that most of the influential film noir pictures were released before the 60's, and I find it very difficult to associate with such films. I suppose I'll go with traditional 'best films' list and choose either Double Indemnity or M.
Comedy: Tough call yet again, as comedy is an immensely broad genre. Now, naturally, Charlie Chaplin is the founder of slapstick comedy... but what about other variations? For political humor, it's easily Dr. Strangelove and MASH. Etc, etc, etc.
Musical: Singin' in the Rain.
War: Yup, definitely Apocalypse Now.
Western: Probably one of Sergio Leone's flicks, like Once Upon a Time in the West and the Good, the Bad, and the Ugly.
Horror/Thriller: Psycho.
Gangster: Gonna have to go with Kovacs (again) here. The Godfather probably wins, but Mean Streets and Goodfellas certainly deserve recognition.
Animated: Snow White is easily the most influential animated movie of all time, even if I can't stand it.
Documentary: Well... I reckon documentaries only became mainstream entertainment as of late, and, ultimately, the format for the modern documentary was established by Michael Moore. I would guess that, if I had to pick a film of his, I'd go with Bowling for Columbine.
Romance: Casablanca.
Fantasy: LotR series.