I've been a big Coen bros. fan since seeing Raising Arizona on a Friday night with a couple of friends when I was 17. Not knowing anything about the film, we were completely blown over by this ingenious and hilarious movie. One of the most transformative moviegoing experiences I ever had. (Either the week before or the week after, we saw David Byrne's True Stories, and there again was this guy John Goodman whom nobody had ever heard of.)
It was tough, but I voted for Blood Simple, the only one I didn't see first-run. I like Chandler and Hammett-type writing, and I respected their feel for the genre and the sheer inventiveness of how they approached it. The originality and feel of that movie just always impresses me.
I always liked The Hudsucker Proxy and was always a little surprised it didn't get more notice. I think it may help to have some familiarity with movies of the '30s and '40s.
I would put NCFOM in second place.
--Justin