I'm also a fan of Mushishi! Though I haven't finished reading the manga yet... The anime is fantastic for sure.
I can't say one anime because there are so many out there that are so amazing. Chihayafuru, Legend of the Galactic Heroes (the original, though the reboot is pretty good too), Hikaru no Go, Shouwa Genroku Rakugo Shinjuu, Yuri on Ice
Honorable mention for Golden Kamuy.
For anime movies, I would say the Revolutionary Girl Utena movie. It's confusing. I had to watch it with the director's notes to understand some parts, but it's really good and the visuals are just amazing.
Here are my comics: