The Last Samurai is an American epic drama movie released in 2003. In the movie, Captain Nathan Algren is hired to train the Japanese army to fight a rebellion by the Samurai. However, he is unexpectedly influenced and impressed by Japanese warriors, putting him at the center of a struggle between two worlds and two eras.
The Last Samurai title on the poster is written in Trajan Regular designed by Carol Twombly in 1989. Trajan is a commercial typeface and you can view more details about it here.