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.
The Good, The Bad, and the Weird (좋은 놈, 나쁜 놈, 이상한 놈) is a fantastic slapstick take on the classic western that has a lot of fun with the setting.
Trollhunter (Trolljegeren) is a great horror-mockumentary done in a found footage style.
Basically anything by Kurosawa.