I first heard about Shall We Dance when it first came out in Japan, and was setting box office records (well, it was a long time ago; I assume that it was, because I can't think of any other reason that I'd've heard of it). My biggest surprise was actually the title. I heard about it in Japanese media, and remember it being called Odorimashou (which is, literally, Japanese for 'Shall We Dance').
But when the movie started, the title shown was 'Shall We ダンス?', that is, the english words 'Shall We' in (script) roman characters, followed by the english word 'Dance' in japanese characters. That's just a weird way to write it, and I have to assume that it was written that way as a deliberate reference to something, although I can only guess what that something was (the song 'Shall We Dance?', from Rodgers and Hammerstein's 'The King and I' was mentioned in the story; perhaps it was written that way when that was first released?).
In any event, I enjoyed the movie quite a lot. As I'd heard, much of it was driven by the social stigma associated with ballroom dancing (perhaps less now? I don't really know) in Japan. I can imagine a number of the scenes being somewhat painful for Japanese people to watch, but it was very poignant overall. And having learned some ballroom dancing since the movie was released, I can appreciate much more of what the characters were thinking while going through their practices and such.
It's decent exercise (actually, it can be damned good exercise, but is rarely done that way, for many reasons (except for jitterbug)), increases your appreciation for music, and is a lot of fun. So I could definitely see why the main characters get into it, even when they didn't expect to do so. Seeing them discretely practicing steps was fairly amusing, too, although their practices seemed to be more on the order of practicing which step to take next, while mine were always more how to take a type of step (stuff like 'rise and fall' in waltz, or using correct cuban motion).
One thing I can't figure out, and I'm not sure that I'll try to find out, is how they thought they could make a US remake. As I mentioned, much of the movie is driven by the stigma attached in Japan. Lacking that stigma here, I can't see how the same story could be at all interesting in a US context. I can't see more than, 'man gets bored', 'man takes dancing lessons hoping to meet pretty teacher', 'wife of man is confused', 'man learns more than expected'. That really isn't much. Not nothing, perhaps, but not much.
But the original was fabulous. It was poignant, as I mentioned, and frequently quietly funny. The relationship between Sugiyama and Mai-chan was deftly handled, and very well acted on both of their parts. The movie is also an interesting window on the Japanese as a people.
I do find myself disappointed that Ms Kusakari hasn't appeared in any more roles, as well as intrigued that she is a ballerina. I'm thinking that she must be awfully tall for a ballerina. But she definitely has the posture and bearing of someone who dances all the time.
In any event, do yourself a favor and watch this one, if you get a chance. You won't regret it.