I've run Space Battleship Yamato using Traveller. Record of Lodoss War is the manga/anime retelling of the author's D&D game.
My games have been influenced by a lot of anime and manga. Right off the top of my head - Bubblegum Crisis, Ghost in the Shell, Appleseed, Ruin Explorers, Legend of the Galactic Heroes, Gundam (a lot, but not all), Cowboy Bebop, Patlabor, Macross (some but not all), Wings of Honneamaise, Evangelion, Samurai X, Goblin Slayer, Samurai Champloo, Akira, The Weathering Continent, plus a bunch of shorts by Katsuhiro Otomo.
I have to admit, some of the stuff I watch with the family just wouldn't really work in a RPG setting. Shows like Genshiken, Comic Party, The Quintessential Quintuplets, Your Name, Belle, A Whisker Away, My Roommate is a Cat, and the Miyazaki films we like.
None of us think that isekai would be fun to play as a RPG session.
EDIT: I'm a big fan of Mekton and Cyberpunk 2020 - R. Talsorian Games had winners with those and the anime/manga influence is huge in them.