It depends on your approach to films. I tend to avoid industry films and entertainment films. I'm not interested in cinema as a business or as a rollercoaster ride; I'm interested in cinema as an art form (even though I have serious reservations about the worth of art (an old PF thread)). I prefer films made by a single artist or a tightly knit group of artists. I would use the term "independent film", but that term has been abused in recent years.
I tend to agree a lot with the film critic, Ray Carney. I wouldn't say I agree with him about everything -- no way -- but I agree with him more than any other film critic. Read about some of his opinions on cinema here:
http://people.bu.edu/rcarney/independentfilm/
I think before you see the latest films, you need to catch up with what you have surely missed -- and that would include some very old films. If you're really keen, I would suggest working through the Criterion Collection:
http://www.criterionco.com/asp/browse.asp
Well-known directors I recommend include:
Andrei Tarkovsky
Ingmar Bergman
Robert Bresson
Yasujiro Ozu
Akira Kurosawa
John Cassavetes
Carl Dreyer
Mike Leigh
A couple of lists of mostly fine directors:
http://www.sensesofcinema.com/contents/directors/index.html
http://www.filmref.com/directors/directors.html
Then there's various genres like silent films (chaplin, griffith, murnau), documentaries, and stop-frame animation (svankmajer, brothers quay).
Maybe I being cynical, but I think I may have just wasted my time with this post. The mainstream view on films is so incredibly entrenched. It's a far different story for music. Go figure.