Walrus1703, I am not as much a fan of Kung-fu films as I am of Japanese films; however, I agree with most of the suggestions here. I also suggest the Japanese films:
When I consider Japanese cinema I classify films into three categories:
Epic: (You simply must see these films)
Ran: 1985- Akira Kurosawa (Kurosawa’s masterpiece, very long and amazing shot re-interpretation of King Lear)
Seven Samurai: 1956- Akira Kurosawa (set the bar for Samurai films and kick started the post WWII Japanese film industry)
Yojimbo: 1961- Akira Kurosawa
The Sword of Doom: 1966- Kihachi Okamoto
Throne of Blood: 1957- Akira Kurosawa (Kurosawa’s re-interpretation of Macbeth)
Zatoichi (Shintaro Katsu’s version): 1989- Shintaro Katsu
Very Good:
Yojimbo: 1961- Akira Kurosawa
Rashomon: 1950- Akira Kurosawa
13 Assassins: 2010- Takashi Miike
The Twilight Samurai: 2002- Yoji Yamada
Samurai Assassin: 1965- Kihachi Okamoto
Harakiri: 1964- Masaki Kobayashi
The 47 Ronin: 1941- Kenji Mizoguchi
Kagemusha: 1980- Akira Kurosawa
Rurouni Kenshin: 2012- Keishi Ohtomo (Live action version of Manga and Anime know in the US as Samurai X, there are three films and all of them were fun to watch)
Samurai Fiction: 1998- Hiroyuki Nakano (not completely serious but fun all the same)
Not completely Japanese but strong ties with the Japanese film industry:
Shogun: 1980- Jerry London
The Last Samurai: 2003- Edward Zwick
And lastly, if you want a fantastic Japanese movie that is not martial arts but feels like Band of Brothers and Pearl Harbor rolled into one film, I suggest:
Yamato: 2005- Jun’ya Sato
Well I am sure there are a ton of others here who can add to this list, hope this helps.