The popular site https://asian-movies-online.com/country/japan has several Japanese movies with English subtitles that you will enjoy. Here are a few popular ones:

1. “Spirited Away” (Sen to Chihiro no Kamikakushi) – Directed by Hayao Miyazaki, this animated fantasy film follows the journey of a young girl who enters a spirit world to save her parents.

2. “Akira” – A sci-fi anime film directed by Katsuhiro Otomo, “Akira” is set in futuristic Tokyo and tells the story of a young biker who gains powerful psychic abilities.

3. “Your Name” (Kimi no Na wa) – Makoto Shinkai’s critically acclaimed romantic fantasy anime film revolves around two high school students who mysteriously swap bodies.

4. “Rashomon” – Directed by Akira Kurosawa, “Rashomon” is a classic Japanese film known for its narrative structure, which presents a murder from multiple perspectives.

5. “Seven Samurai” (Shichinin no Samurai) – Another masterpiece by Akira Kurosawa, this epic historical drama follows a group of samurais who defend a village against bandits.

6. “Departures” (Okuribito) – A touching drama by Yojiro Takita, “Departures” delves into the life of a cellist who starts working as a funeral professional.

7. “Battle Royale” – Directed by Kinji Fukasaku, this dystopian thriller portrays a class of high school students forced to fight to the death on a deserted island.

These are just a few examples, and there are many more Japanese movies across various genres available with English subtitles.