The first remake that comes to my mind is the horror movie Ring that was based on the japanese movie Ringu and maybe we could call a remake the Ghost in the Shell movie that was based on an anime with the same name. The Fistful of Dollars western movie was heavily inspired by Kurosawa's Yojimbo or The Magnificent Seven by Kurosawa's Seven Samurai. The Star Wars admittedly drawn inspiration from Kurosawa's The Hidden Fortress, Kill Bill from the movie Lady Snowblood and the Full Metal Jacket from the second film of The Human Condition triology called Road to Eternity . And so on so on...