Every time someone asks me this question I want to say: "Ok, have a seat." because the answer will take a moment. I have one movie that immediately comes to mind as the, in my opinion, best movie but calling that one my favourite isn'y really fitting, you'll see why when I get to that.
Instead of one single favourite movie I have several "best of genre or mood" type of selections. Here we go:
Science Fiction: "2001: A Space Odyssee"
Classic, slow science fiction that leaves tons of room for interpretation. I tried watching Andrey Tarkovsky's "Solyaris" but that is way beyond what is still enjoyable for me. 2001 is just right in that regard, it asks some interesting questions but is still an entertaining film.
Yes, I consider "Star Wars" fantasy, not science fiction. Deal with it.
There's not much else to say about this one, it's widely regarded the best of the franchise and for good reason. While "A New Hope" is telling a classic hero's tale very well, it's characters are a bit flat. "Return of the Jedi" has some of the best scenes of the series but suffers from having a bit too much going on. "Empire" contains most of the interesting character development of the three films while still feeling well confined and tightly structured.
Thriller/Drama: "Léon" (a.k.a. "The Professional")
The acting and directing in this movie is just so damn good. Every line and shot are so incredibly spot-on. It tells an engaging story with interesting and relatable characters and it's still engaging even after multiple times watching it.
It's my favourite Luc Besson movie and has the best performances of Jean Reno, Natalie Portman and Gary Oldman that I know of.
When I first saw "Alien" I was twelve years old and I had nightmares for weeks. Now I'm 30 and it still get's me every single time.
Apart from some high quality acting, it does one thing especially well: not showing the monster which makes it so much more terrifying.
Action: "Mad Max: Fury Road"
The most recent addition to this list. When it comes to pure action movies, this one is executed perfectly. It's essentially a two hour chase scene that almost never stops and never gets boring. This movie just keeps being exciting for its entire runtime. Exactly what an action movie is supposed to do.
Happy Movie: "WALL-E"
Whenever I need that feeling of a warm blanket from a movie, this is it. Something about it just pulls the right strings.
It's also a very well made film with surprisingly little dialog, which I always enjoy very much.
Sad Movie: "Grave of the Fireflies"
What a gut wrenching movie. This story about two children trying to survive during World War II in Japan is one of the saddest, most tragic things that I know. Despite being a very good movie, I have seen it exactly once and I'm not sure, if I can watch it again.
Silly Movie: "Pacific Rim"
Giant robots, giant monsters. Nothing to add. this movie is really fun, just don't think about it too hard. Although, it has some really well done scenes.
Now, as I mentioned, there's one movie that immediately comes to mind when people ask me for my favourite film. The thing with this is that it's a movie that is I don't actually enjoy and that completely ruins the day when I watch it so "favourite" isn't the right word. Still, it's the best piece of filmmaking that I have ever seen: