Captain Phillips -- Greengrass turns down the 'shaky cam' and turns up the tension. Over two hours just flew by. Even though I knew how it was going to end, it was still very enjoyable. The final few minutes were improvised on the set, but might be the most powerful moments in the film.
Gravity -- The best technical exercise I've seen in years. The opening shot is marvelous (even if it's a little too dependent on CGI trickery). I still think that Children of Men is Cuaron's best film, but this might be the most intense 90 minutes I've spent in a theater.
This Is The End -- My favorite 'dumb comedy' of the year. The stars play amped-up parodies of themselves, and you can't help but laugh at how much fun they have with the script and setting.
Warm Bodies -- One of the better mainstream teen comedies I've seen in a while, and it managed to do something a little different with the zombie genre too. It possesses a gory heart of gold, and was a lot better than the trailers let on.
Films from 2013 that I still really want to see (in alphabetical order):
12 Years A Slave
The Act of Killing
All Is Lost
Dallas Buyers Club
Inside Llewyn Davis
Safe Prediction for 2014 -- The Raid 2 will kick every single ass.