One reason I like Nodame Cantabile's Chiaki
One of reasons that I like Chiaki is that he is that rarity in anime, a competent protagonist who understands his own competence. The usual pattern is that the protagonist is either unskilled (and learns through the course of the anime) or is basically an idiot savant, ferociously skilled but without understanding.
(Nodame herself is an example of the latter category, and one of the themes throughout Nodame Cantabile is people trying to get her to harness and direct that ferocious skill, to think about and understand what she is doing.)
One particularly blunt way to put the attraction of this is that it means that Chiaki has clues. He comes to realizations; he sees problems; he fixes things. In short, he gets to act intelligently, not blindly. He gets to be smart in his field, which is refreshing to see.
(This is unfortunately kind of a rarity in anime protagonists; being smart this way is usually reserved for the secondary characters.)