The challenge with this thread is to explain why it is we like our favourite films. It's too easy to just say you like this or that, but to make it interesting a deeper explanation is needed and that can be quite hard.
A lot of the time I'm drawn to a film just because I fancy the actor in it, like Leonardo Di Caprio, Keanu Reeves, Ewan McGreggor and Arnie (when he was younger). They mostly do action films. I like a lot of action films, but I can't tell how much of it is the story and how much is the actor.
Faves are: Conan the Barbarian (cos I would rather be a barbarian than civilised!), Predator (the lone hero idea) and The Running Man. This has a political point to it and great tongue-in-cheek sci fi plot. It shows mass manipulation of TV audiences and how the state is making the good guys out to be the bad guys.
Rambo First Blood is good too and shows how Vietnam vets were treated with contempt when they came back home. Action films with state or secret society conspiracies in them appeal. There are quite a few of them.
Also Mad Max appeals to my sense of a coming dark age and how people would have to be barbaric to survive.
Monty Python is fantastic (apart from I don't like some of the smut). They were so innovative. (But does everyone agree that Mel Gibson's remake of the classic "Life of Brian" is not as funny as the original?) Films like Excalibur, seem to owe so much to being preceded by Monty Python and the Holy Grail.