If not favorite, ones that touched you in some way.
I'll start by mentioning some movies from my mother tongue(Malayalam of Kerala, India):
- Mumbai Police
A crime thriller (Came out almost 2 decades ago n was very striking for the time)
- KammaraSambhavam
Political/Historic satire/drama (The main actor has some cases on him, but the movie is quite good)
- Kathavasheshan
- Devasuram
Conservative sigma male upper class Kerala dude getting character development. I really liked how the transformation happened in it
- Maheshinte Parthikaaram (Mahesh's Revenge)
Not an action movie.
From my country, but not in my mother tongue:
- Super Deluxe - A Tamil movie that I recently watched, quite unique
- Enthiran (Robot), a Tamil movie
Has over the top stuff, but is fun to watch
- Viduthalai(Liberation), another Tamil movie
- Agent Vinod - A Hindi spy-comedy movie
The anime that I like are Hunter x Hunter, Parasyte, Samurai Flamenco, Gintama.
Hardly a deep cut, but Crouching Tiger Hidden Dragon is absolutely fantastic.
A master of mystical superhuman martial arts is trying to retire, but a suspiciously talented thief keeps making off with his unbreakable sword. The movie is sold on and remembered for its acrobatic and set-destroying fight scenes, and if you just watched those highlights, you'd have a decent time. But you'd miss the clever characterization, the gorgeous cinematography, the excellent score, and on and on and on. If you just want wire-fu then watch Iron Monkey. This is a movie about all the small moments between complex people. It opens with ten minutes of dialog on purpose. The combat is what happens when characters fail.