I want it to have something original and different. It could be in the script, the directing, or an acting performance. At least one of those should be something different and new. It could be in all of those, and that would be really special. I hate it when movies don't let me think or feel for myself. Perfect example was Saving Private Ryan. Most of the movie was exceptional. It told a story and was great to look at. But Spielberg didn't trust he'd made a good movie, and ruined at the end trying to pull on the heart strings and show the audience how they should feel. The movie was good enough that it didn't need that sappy crap to make people the emotions. The story would bring it out naturally.
I feel the opposite. Every other movie is already set in New York...not really anything new a movie can give me by being set in NYC. I prefer movies set in random places I'm not too familiar with, especially when care is taken to present the setting. The Coen Bros. do a good job of this, Southwest Texas (No Country), North Dakota (Fargo), etc. Anyway, Cinematography is huge for me. Camera angles, colors, etc. If a movie doesn't look good, it's already fighting an uphill battle. Also, I usually like movies to have a little bit of a dark side/grit to them. Those movies make more of an impression and seem more realistic than light-hearted fare (though I still enjoy those types of movies too...just usually not as memorable). Children of Men was one of my favorite "recent' movies like this. Last, movies that often stick with me the most are the mind-bending types that leave a lot unanswered and keep you thinking about them long after the film is over (Inception, Mulholland Drive, Brazil).