The best Japanese movies I've seen have other genres but lets see...
* Crows Zero 1 & 2: definitely a MUST SEE, they're not romantic on any way though. The cast is 99% male and most of the movies goes into fight scenes, but they are a jewel from the "artistic" point of view so I recommend it anyway.
* Koizora: if you're looking for drama and romance then THIS. Lots of both. There's also a drama with the same story but I prefer the movie.
* Air Doll: a not ordinary romance but, well, if you want something unusual, weird and more mature then give it a chance.
* Paradise Kiss: they did a great job on the production for this one.