Best romantic anime is Kare Kano. In my opinion, I've seen nothing even close. The first season is one of the most original and brilliant pieces of media I've ever seen. Hilarious one minute and then melancholy and thoughtful the next. There is still nothing like it. Screw NGE, Hideaki Anno missed his calling as a shoujo directer.
The characters have depth and, despite appearing to be outwardly in control of their lives, they both have issues that influence their motives and responses to the world. They hurt each other, they get mad at each other, and they misunderstand one another like real people. They battle with their own insecurities. It's amazing to watch after one of the cardboard romances in most anime. The chase scene was fucking incredible. Yukino is one of the best, most interesting characters in all of anime.
Second place is Kimi ni Todoke. Very heartwarming and positive.
Third is Nodame Cantabile. The setup of one falling in love at first sight while the other fights against falling in love the entire way is golden. That they are almost exact opposites makes it even better.
Best couple, though, I'm giving to the MC and Misaki from Welcome to the NHK. They are both so screwed up that they could not be more perfect for one another. It's part of the reason that it's one of the best anime in the history of anime.
