^ I would also throw Red Cliff in there, but you should have some knowledge about chinese history (end of Han dynasty) for that (and it's very long, especially in the 2 part version)

I'd say Japan, they got the all-time classics courtesy Kurosawa. Chinese cinema, at least from what i have seen, often compromises depth for entertainment. And also, Anime cannot be discounted, not just becaause of Studio Ghibli, but because of gems like Wings of Honneamaise, Jin-Roh the Wolf's Brigade, pretty much anything from Satoshi Kon. Anime accounts for some of the finest Asian cinema I have seen. Though I have immensely enjoyed a lot of Chinese cinema(Wuxia stuff, John Woo - Chow Yun Fat collaborations freely come to mind), id say Japan wins it for me on overall quality and having a bit more depth to it.

Hong Kong cinema for action. (Jackie Chan 70's and 80's films were far superior to his toned down Americanised mid 90's and onwards stuff).
Mainland Chinese for mythical stories (Hero, CTHD, HOFD).
Korean for thrillers (The Vengeance Trilogy are one of my favourite films of all time).

Honk Kong/China movie by a mile, no contest. No Asian country have produce more house hold name then China.

Chow Yun Fat
Jet Li
Jackie Chan
Sammo Hung
Michelle Yeoh
and these are just the actors.

We got John Woo and Ang Lee as Hollywood big directors. NO CONTEST!!!

Ah, Jin Roh. I hate to say it, but it is an older movie, from the 90s. I would interprete the 'Who makes the best movies?' as talking about the present, and Akira Kurosawa is no longer alive. And well, all movies are for entertainment (including Akira Kurosawa and Jin Roh). I think you mean shallow entertainment. And for that you can not say chinese movies are only shallow. Try flowers of war or something like that. Basically Zhang Yimou was never about shallow entertainment (red lantern). And you didn't even mention Korea and the excellent Park Chan-Wook.

All time? Honk Kong/China easily
At the moment? Korea easily.

Jackie chan in the 70's and 80's was unstoppable. His movies were incredible.

Japan. Battle Royale and Ring are great films. The American version of The Ring was shite!

Indian movies had a great influence on my childhood.. Now I don't watch any asian films, but i've heard that korea is now leading this field..

China shouldn't be able to compete as anything too groundbreaking ends up banned in its home country. A movie can't be to political and it can't be too dark or else BAN. You can pretty much only make war and martial arts movies.