I tend to favor movies that could be described as heavy, dark, stylized, clever, and/or offbeat.
I don't like silly action movies with fast cars and big explosions. I want my action movies simple and to the point. This is not the genre to try and pull off complex and subtle plots (i.e. Pitch Black was great, the sequel was fucking trash).
I don't care if the movie has 100 million dollars worth of special effects. There had better be some plot to back that up. I'm a sucker for a fantastic visual, but that and fifty cents worth of plot will get you Silent Hill.
I don't like stupid slapstick comedies catering to the beer 'n tits crowd. I want my comedies offbeat if not outright strange. John Cusack is a plus. The likes of Will Ferrell, Jim Carrey, and Jack Black are almost automatic disqualifications.
Some of my favorite dramas are those I never want to see again except to show to someone else. These movies are emotionally powerful and thought provoking, but not fun to watch in the usual sense. Too many modern "dramas" are, in fact, about nothing at all. Dramatic tension is key.
With horror movies I am looking for a specific feeling of being... unsettled somewhere inside. Movies that are all about things jumping out of the screen are fun from time to time, but I am always trying to recapture the feeling I got as a young man reading my father's Lovecraft novels, of something vast and malevolent moving just under the surface of things, that we can never understand fully but only understand how powerless and insignificant we are. Horror that focuses on claustrophobic or paranoid feelings works for me as well. John Carpenter has done a number of good films around these themes.