I can name movies I truly enjoy, or movies I think everyone should watch at least once. But I can't actually name a favorite movie.
I had this dilemma. Whenever someone asks a question like this, I generally just go with the first one that pops into my head but that's not very reliable.
Imagine that you're going to a desert island for the next five years, which has all the food you can eat, and a nice home theater with no satellite services, cable, etc. Just a Blu-ray player. Now, you can take 10 movies with you. I think such a question gets to the heart of the matter. What movies would you bring? In the end, it boils down to those movies which give you undiminished pleasure in watching over and over. Take a stab at.
I'd probably just take Cast Away and think about how hilarious I am for 5 years.