Oh, this nodeshell I have to rescue!
This was the 1995 animated movie from Studio Ghibli, directed by Yoshifumi Kondo and produced by Hayao Miyazaki. The official English title is Whisper of the Heart, though the more literal translation If You Listen Closely is also often seen. Like My Neighbor Totoro, it is one of those films that make you cry because they're so beautiful - which is odd because it plays in a modern Japanese city, usually everything but beautiful.
The film revolves around Shizuku Tsukishima, a 14 year old girl who is a veritable bookworm. Through the books, she meets Seiji Amasawa, a boy her age with the ambition to become a violin maker. The admiration Shizuku feels for his dedication to that aim causes her to seriously try and realize her own ambition of becoming a professional writer. With her imagination fuelled by the figurine of a cat she sees in Seiji's Grandfather's antiquities shop, she sharpens her pencil and starts writing...
First and foremost, this is a movie about the familiar theme of growing up (played out very unpretentiously and unspectacular, yet deeply touching), but it's also about the magic of human imagination and its main medium, books. And finally, it shows how life in a modern, ugly city full of narrow streets and cramped apartments (unlike most anime, where everyone seems to be rich enough to afford huge houses, the movie is very realistic in that respect) can still be as full of wonder and beauty as the countryside with its Totoros and Tanuki. Speaking of Tanuki, apparently the opening shot of "Mimi o Sumaseba" is exactly the same as the closing scene of Heisei Tanuki Gassen Pompoko - a rather strange statement about this world of ours.
Anyway, the film is beautiful; go watch it.