Ai Yori Aoshi is easy to compare to another harem/romantic comedy, Love Hina, and in some ways this is not without merit. The heroine, Aoi, is unquestionably similar to Love Hina's Shinobu right down to hair style and temperament. However, Ai Yori Aoshi doesn't have the same manic craziness that Love Hina does and is much sweeter to the point of being saccharine.
The primary failing of Ai Yori Aoshi is its main characters. The hero, Kaoru, is a nice guy, and that's about all you can say about him. He's just really nice, which means he's boring to watch since he has no real flaws.
His bride-to-be, Aoi, is nice and obsessed. She's essentially lived her entire life dreaming about Kaoru, fantasizing about doing all sorts of mundane domestic chores for him, despite the fact that he's totally forgotten about her since their first meeting. While the story never clarifies exactly how well they knew each other as children, it seems as though it might have been as limited as one visit.
In either case, the young Aoi is somehow impressed enough to devote her life to him while he moves on to live life. This obsession makes Aoi a relatively boring character as she's defined by Kaoru; happy when he is, sad when he is, and always talking about how she dreamed about doing his laundry or hugging him, etc., usually accompanied by a fountain of tears. The couple never really has any problems. There's usually a minor misunderstanding or expressed desire by Aoi which is quickly worked out. Unfortunately, in doing this, the series usually sways from romantic to overbearing.