This is a pretty hard question to answer because normally people have a bunch of favorites but if we divide the movies into genres it should be easier, if you don't have one favorite movie per genre then add as many as you like or just write Undecided.
(In no particular order)
Martial Arts: Yip Man 1&2.
Action: Training Day, Inception, Gladiator, Sherlock Holmes, Matrix 1&2, Transformers 1&2, X-Men (all of them).
Crime: American Gangster.
Drama: The Shawshank Redemption, The Prestige, Gran Torino, The Green Mile.
Adventure: Lord of the Rings (all of them), Indiana Jones (all of them), Avatar, Kingdom of Heaven, Django Unchained.
Naturally there are a bunch of other movies I wouldnt mind watching over and over again however if I were to include every movie it would take to long so this is a list of movies that I really liked. Only in the Martial Arts genre can I say that Yip Man is my favorite movie, the rest of the genres have bunch of movies that I consider my favorite.