Here goes, I will only post FIVE because that was the title of the thread... but there are so many that I've watched and could choose. Why do I like these movies? Real simple... I relate to some element of the humanity in the characters, and there is usually (but not always) action and cool special effects. There is also usually a philosophical struggle or statement underlying...
1. Watchmen - This movie does a BRILLIANT job of making super heroes more "real" (though ok, it was actually made in comic beforehand... but that just means it was well thought out, right?). From the abused super woman (Silk Spectre) to the all-powerful, yet detached and almost narcissistic Dr. Manhattan, this movie puts a great human face on the superhuman. Also, I really dug how the comedian's personality was pieced together through the memories of the other characters... and how you learn the most about his humanity from his arch enemy... what a trip.
2. Sonatine - This Japanese mob movie by Takeshi Kitano (i.e. Beat Takeshi) is my favourite by him. If anyone follows his movies, you know they oscillate between quiet and violence very quickly. The bond that you build with the characters in this movie as they find respite on the shores of Okinawa is strong. My opinion of this movie was sealed at the same time that you find the ultimate empathy for the main character (mob boss played by Kitano himself)... right at the end
3. The Dark Knight Rises - People have listed the Dark Knight tons of times in this thread... perhaps this is a vote of defiance, I think the 3rd movie in the Dark Knight series is the best. Yes, it doesn't have Heath Ledger in it as the joker (who was crazy good... but could you honestly relate to the character? They tried, they really did, but in the end its a negatory from me), however the social statement regarding the general chaos and rioting that could so easily be inserted into society by a few devious minds really reverberated with me at the time.... it was reflective of not only terrorist ideology, but also strangely (intentionally?) close to the occupy wall street messaging at the time. At the same time, the psychological torture that the Dark Knight himself endures really speaks to me.
4. Forrest Gump - Hanks rules. The emotional obstacle course that we are taken through, which the main character is oblivious to, just makes this movie all that more special. And ironically, though the viewers recognise the main character as someone who would never fully be capable of understanding them, they deeply empathize with him.... the perpetual underdog. Could easily have put castaway here as well.
5. The Breakfast Club - Perhaps I'm a product of a generation here... but this is basically a stand-in for any John Hughes movie. The characters in these movies just take me home ... the Norman Rockwell of the movie biz....