Nodame Cantabile

Winner of the 2004 Kodansha Manga Award.
From Del Rey:
The son of a famous pianist, music student Shinichi Chiaki dreams of studying abroad and becoming a conductor like his mentor. Unfortunately, his fear of flying grounds his lofty plans! As he watches other classmates achieve what he has always wanted, Shinichi wonders if he should quit music altogether.
Then one day he meets fellow student Megumi Noda, also known as Nodame. This oddball girl cannot cook, clean, or even read a music score, but she can play the piano in incomparable Cantabile style. And she teaches Chiaki something that he has forgotten: to enjoy his music, no matter where he is.