Akira Kurosawa
Certainly the best known Japanese director in the West. Essentially all of his films are on DVD for Region 1, and apparently they are nearly all on Hulu.
X 1943 Sanshiro Sugata
X 1944 The Most Beautiful (Ichiban utsukushiku)
X 1945 Sanshiro Sugata Part II
X 1945 The Men Who Tread on the Tiger's Tail (Tora no o wo fumu otokotachi)
X 1946 No Regrets for Our Youth (Waga seishun ni kuinashi)
X 1947 One Wonderful Sunday (Subarashiki nichiyōbi)
1948 Drunken Angel (Yoidore tenshi)
1949 The Quiet Duel (Shizukanaru ketto)
1949 Stray Dog (Nora inu)
1950 Scandal
X 1950 Rashōmon
1951 The Idiot (Hakuchi)
X 1952 Ikiru aka To Live
1954 Seven Samurai (Shichinin no samurai)
1955 I Live in Fear (Ikimono no kiroku)
1957 Throne of Blood (Kumonosu-jō)
1957 The Lower Depths (Donzoko)
1958 The Hidden Fortress (Kakushi toride no san akunin)
1960 The Bad Sleep Well (Warui yatsu hodo yoku nemuru)
1961 Yojimbo
1962 Sanjurō
1963 High and Low (Tengoku to jigoku)
1965 Red Beard (Akahige)
1970 Dodesukaden
1975 Dersu Uzala
1980 Kagemusha
X 1985 Ran
X 1990 Dreams aka Akira Kurosawa's Dreams
1991 Rhapsody in August ( Hachigatsu no rapusodī)
1993 Madadayo
Ironically, I stopped at 1948, just when Kurosawa starts getting really good. Oh well, something to look forward to, perhaps this summer. Of the ones I've seen, Ikiru is the most profound, maybe even life-changing for me. I'll write about this in more detail when I get around to watching it again. (Just a quick note that Roger Ebert (RIP) really loved this film.) Rashōmon is quite the mind-bender, but the problem was that while it was an incredibly fresh idea in 1950 (unreliable narrators being more of a staple of fiction and not movies up to that point), it has lost some of its potency just because of the many (often inferior) films that borrowed from it. Still quite an achievement, however. If I am recalling correctly, Kurosawa went a little overboard at the end of the shoot and overdid it with the artificial wind and rain.
I've only seen Ran and Dreams on the big screen (Dreams in its initial US run incidentally). Definitely worth catching Ran on the big screen, and I hope to again some day, along with Seven Samurai (if I have an entire afternoon free!).
Yasujirō Ozu
I've tried to reformat the Ozu filmography from wiki just a bit (though it may not display well at all), and then indicate whether it is available in Criterion/Eclipse put it out (meaning it is Region 1) or BFI (meaning it is R2). R3 means basically only available in that region (and the subtitles may be really lacking). To fully follow Ozu and the other directors below, you need to invest in a region-free DVD, which is not really the case for Kurosawa.
1929 Days of Youth BFI Student
1930 Walk Cheerfully BFI Gangster
1930 I Flunked But... BFI Student
1930 That Night's Wife BFI Gangster
1931 The Lady and The Beard BFI Student
X 1931 Tokyo Chorus Eclipse 10
X 1932 Otona no miru ehon ... aka I Was Born, But... Eclipse 10
1932 Seishun no yume imaizuko ... aka Where Are the Dreams of Youth? BFI Student
1932 Mata au hi made ... aka Until the Day We Meet Again
1933 Tokyo no onna ... aka Woman of Tokyo BFI Melodrama
1933 Hijosen no onna ... aka Dragnet Girl BFI Gangster
X 1933 Dekigokoro ... aka Passing Fancy Eclipse 10
1934 Haha wo kowazuya ... aka A Mother Should Be Loved (incomplete) R2/R3
1934 Ukikusa monogatari ... aka A Story of Floating Weeds Criterion (232)
1935 Hakoiri musume ... aka An Innocent Maid
1935 Tokyo no yado ... aka An Inn in Tokyo R3
1936 Kagamijishi
1936 Daigaku yoitoko ... aka College Is a Nice Place ... aka Tokyo Is a Nice Place
1936 Hitori musuko ... aka The Only Son Criterion (524)
1937 Shukujo wa nani o wasureta ka ... aka What Did the Lady Forget? R2/R3
1941 Todake no kyodai ... aka The Toda Brothers and Sisters R3
1942 Chichi ariki ... aka There Was a Father Criterion (524)
1947 Nagaya shinshiroku ... aka The Record of a Tenement Gentleman R3
1948 Kaze no naka no mendori ... aka A Hen in the Wind R2/R3
1949 Banshun ... aka Late Spring Criterion (331)
1950 Munekata kyoudai ... aka The Munekata Sisters
1951 Bakushû ... aka Early Summer Criterion (240)
1952 Ochazuke no aji ... aka Flavor of Green Tea Over Rice R2/R3
1953 Tokyo monogatari ... aka Tokyo Story (USA) Criterion (217)
1956 Soshun ... aka Early Spring (USA) Eclipse 3/BFI
1957 Tokyo boshoku ... aka Tokyo Twilight Eclipse 3/BFI
1958 Higanbana ... aka Equinox Flower Eclipse 3
1959 Ohayô ... aka Good Morning Criterion/BFI
1959 Ukigusa ... aka Floating Weeds Criterion (232)/BFI
1960 Akibiyori ... aka Late Autumn Eclipse 3
1961 Kohayagawa-ke no aki ... aka Early Autumn (or The End of Summer) Eclipse 3
1962 Sanma no aji ... aka An Autumn Afternoon (USA) Criterion (446)
I've watched very few of these films, mostly the early silents, though I own quite a number of them. Criterion/Eclipse has done a really good job of the later films (past 1950) and they also released some early Family comedies and The Only Son/There was a Father (I kind of hoped they would have included the incomplete A Mother Should Be Loved, but they didn't do so). In general, BFI has done a better job collecting the early surviving Ozu films. The Student Comedies is probably the best value with four early films, including I Flunked But... . BFI has just released The Gangster Films, which includes Dragnet Girl and Last Night's Wife. I have to say, the price is a bit steep for fairly marginal films in Ozu's discography, but I may eventually spring for them.
I am also still torn over Three Melodramas, which contains Woman of Tokyo, but then two other films available from Eclipse (the Late Ozu box). The price would have to drop quite a bit. I've just noticed that BFI has paired A Mother Should be Loved with Late Autumn (also in the Late Ozu box), but the price is a bit better and I may eventually pick this up, despite the overlap.
Mikio Naruse
He is clearly the least known of the three in the U.S., mostly because his work is so hard to find (legally anyway). Criterion/Eclipse does have his early surviving works, which I have actually watched and When a Woman Ascends the Stairs, and Masters of Cinema and BFI in the UK (Region 2) have released two box sets of 6 films total (with overlap of Woman Ascends unfortunately).
Thus, this is all that is out on DVD with English subtitles:
X Flunky, Work Hard (Koshiben ganbare, 1931) R1
X No Blood Relation (Nasanu naka, 1932) R1
X Apart From You (Kimi to Wakarete, 1933) R1
X Every-Night Dreams (Yogoto no yume, 1933) R1
X Street Without End (Kagirinaki hodo, 1934) R1
O Repast (Meshi, 1951) R2
O Sound of the Mountain (Yama no oto, 1954) R2
O Late Chrysanthemums (Bangiku, 1954) R2
O Floating Clouds (Ukigumo, 1955) R2
O Flowing (Nagareru, 1956) R2
O When a Woman Ascends the Stairs (Onna ga kaidan o agaru toki, 1960) R1/R2
I am not going to post this entire list, but he has 30+ surviving films (list at Wikipedia). To me this really suggests a market failure. Most of his later films are not available, and virtually none of his works from the 1960s, which are highly regarded (well, curiously I read recently that his 1950s films may be his greatest achievement). In any case, I can only hope that Criterion is working on an Eclipse set of his 1960s films; I would snatch that up as soon as I knew the street date.
I've actually only watched the silent Naruse so far. Street Without End had some good moments, though I think my favorite was Apart From You, which is about a famous actress who wants to be reunited with the child she gave up for adoption.
I've sort of been saving the more sophisticated "talkies" for later, and I will most likely watch them in order. Maybe some day his color films will be released. Now some of the other films are on Hulu (up to 13 apparently), but that doesn't do me much good at the moment. I think it is a bit more likely that someone puts these out on DVD before Hulu comes to Canada, but we'll see.
Kenji Mizoguchi is another figure only partially well served by Criterion/Eclipse and then Masters of Cinema/Eureka. I would say that at least his final works, as well as those films generally regarded as his best, are out on DVD, and I don't think you can say that about Naruse. Since I don't have as many films to catch up on with Mizoguchi, I won't bother listing them. I really thought Street of Shame was incredible, though depressing. I also enjoyed (if that's the right word) Sisters of the Gion (Gion bayashi). The only film I didn't care much for in the Fallen Women box was Women of the Night, which was far too melodramatic, even compared to the others in this vein; it was frankly unbelievable when one of the characters seemed about to get into a "rumble" with some street prostitutes (I think I am remembering this correctly). Of the available Mizoguchi, the main one I still need to watch is Ugetsu, though I probably also ought to also get around some day to Sancho the Bailiff.
Edit (Jan 2023): This article discusses some of the later Naruse films. I think I did track down Scattered Clouds (1967), which is not the same as Flouting Clouds (1955). I don't think I've found Autumn Has Already Started (1960), A Wanderer's Notebook (1962), or Yearning (1964) or, for that matter, Sudden Rain (1956), which again just speaks to a real market failure. It's a shame that you have to turn to the grey market for these films. I think I'll try to actually watch a few more of the 50s films I do own before ordering anything more.