Shoujo Yoshitsuneden

An ordinary second-year high school student is on a class field trip to Kyoto, the heart of traditional Japanese culture. One night, as a penalty for losing a game to some of his friends, he is forced to attempt to sneak into the girls' bathing area to peep on them. However, he is caught, and falls into the bath, suddenly being surrounded by a strange light. When he comes to, he finds that he has somehow been transported back in time to the late 12th century, at the twilight of the Heian period of Japanese history. Having been dragged into this crucial historical period, he is forced to come to terms with what to do, while also struggling to understand why he was transported back eight centuries in time...

Shoujo Yoshitsuneden (lit. The Tale of the Yoshitsune Girl) is a tactical RPG with romantic & visual novel elements. The game's structure is broken up into chapters, and the story is primarily told in the visual novel format, with battle sequences being interspersed throughout. The (nameable) protagonist can also pursue relationships with the various heroines, and the game's ending hinges on which one the player has chosen to become the most intimate with, making for six possible endings.

[from MobyGames]