I'm movie-mad and have a big collection so please bear with me, I am trying to keep it brief!
Some of my favourites are:
Drama - Talk Radio, The Dark Knight Rises, Barfly, Warrior and Whiplash.
Sci-Fi - The Matrix, Alien 1 and 2, Pacific Rim.
Thriller - Silence of the Lambs.
Romance - Dogfight, Notting Hill.
Comedy - Pirates of the Carribean, Buffalo 66, There's Something About Mary.
There are many more I like, too many to mention. My favourite recent movies are Whiplash, Dallas Buyer's Club, Warrior, Dan in Real Life.and 127 hours.