Film: The Girl Who Leapt Through Time (2006)
Director: Mamoru Hosoda
Description: When 17-year-old Makoto Konno gains the ability to, quite literally, "leap" backwards through time, she immediately sets about improving her grades and preventing personal mishaps. However, she soon realises that changing the past isn't as simple as it seems, and eventually, will have to rely on her new powers to shape the future of herself and her friends.(source: Anime News Network)
Personal Note: A small piece of trivia - The film was released without much fanfare in Japan, in a limited number of theaters and wasn't expected to do good business. But according to IMDB.com, the film ran "for days in a row, film-goers would fill the theater, some even standing to watch the film.".
So do yourself a favor, don't read the reviews, don't read all the stuff in wikipedia, just come to the screening and experience the movie first hand.