Movies with a story, but not some generic, cornyass story, but something that gets you thinking "huh, I wonder how this will play out". Have characters with different personalities, unique fight scenes, a climatic end, trying to avoid cliches and actually pretty damn interesting.
If it aint action, blow the audience mind's away. Not overthetop, but something that gets them in a certain way. Make them analyse the character and have them wondering what are they going to do next or "How is he/she going to handle this situation" and the results should not be ordinary, while still being an actual choice.
i havent seen "15 minutes" or "carrot tops chairman of the board" but i definately agree on the rest. (me points to prides post)
I'd also add "Fear and Loathing in las vegas" to that list
To me, for a film to be a really good movie, its gotta be comming from a different angle than usual, i hate thinks that are terribly linnear. I like to be able draw my own conclusions from a film, and its annoying when it all just points to one clear cut - obvious conclusion. However, sometimes , it just doesnt work that way for some films and i still enjoy them, but then, i think it becomes more about the characters in the story, how you can empathise with them, inner struggles, huge changes in characters, all that kind of stuff, doesnt have to do with the plot but it adds an extra dimention to the story.
Oh and if anybody here doesnt mind black and white japanese films, you should check out Akira kurosawa (director/writer) he's got a lot of awesome movies, my favs are:
Rashomon (based on an old japanese story i think.. cant remember though)
The Hidden Fortress