It really doesn't get any better than this for a romance anime! Nodame Cantabile is the story of Megumi Nodame, a pianist at a music conservatory, her trials and tribulations with music and love. It's very well done animation-wise, even to the point of correct fingerings and playing technique for the various orchestral instruments, a time consuming task I'm sure. All the musical performances are also spot-on. They even had an orchestra record pieces specifically for the anime.
Still, none of this matters if the characters and story aren't just right. And mangaka Tomoko Ninomiya got it pitch perfect! It's easy to see why this was so popular in Japan, even inspiring a pretty good live action drama version, though I think a lot of the more comedic elements work better in the anime.