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Damn, I used to give romance-anime recommendations all the time, not sure why I stopped.
Cross Game - Fits your bill perfectly, be ready for some heartbreak though.
Kare Kano - personally my favorite Romance series, the romance is there right from the start, but they go through their relationship gradually and realistically
Crest of the Stars/Banner of the Stars - beautiful romance flourishes slowly in an interesting setting, one of the all time classics
Emma - a classic of the romance genre, love between different classes in Victorian England, a must see
Toshokan Senseou - really fun series, movie coming out this summer. The two main characters start out with a wall between them, and gradually grow closer.
Maria-sama ga Miteiru - if you aren't afraid of lesbians, you may want to check this out, many love stories come together in a very special school
Honorable mentions: Koi Kaze, Honey and Clover, Nodame Cantabile, Saikano