Everyone has their favorites and these are some of mine. I don't do rankings, and this is subject to change at a whim. Freely associated and in no particular order, starting with the directors who are the three 800 lb. gorillas of Japanese cinema:
Seven Samurai (1955, directed by Akira Kurosawa). This was my gateway into Japanese film beyond the Godzilla movies of my youth (and, hey look! It's from Toho, too!). There are Kurosawa films that I like more than this, actually, but there aren't any to which I return more often. It's a big box with everything in it, a film that's actually too short at three hours long.
Ugetsu (1953, directed by Kenji Mizoguchi). Ordinarily, I don't care for Mizoguchi. I find him to be the most manipulative of any legitimately great director. You can generally see the wheels of the plot turning as you watch. And yet, I can't take my eyes off of Ugetsu. Because it's a ghost story, there's a certain formalism to the manipulation that makes it rather more palatable to me, and lends it the power to break my heart.
I Was Born, But...(1932, directed by Yasujiro Ozu). Later Ozu is too rigidly formal for my tastes (although, not so formal that he's above fart jokes in Good Morning, which, coincidentally, is a remake of this film). Early Ozu, on the other hand, seems positively antic in comparison. This is my favorite of his early films, in part because I was raised on the best of the Little Rascals shorts, and this film is like one of those shorts writ large. It's funny and touching at the same time.
Stepping away from the shadow of the Kurosawa/Mizoguchi/Ozu axis, here are some of my other favorites:
Onibaba (1964, directed by Kaneto Shindo), which strikes me as some kind of missing link between I Walked With a Zombie and The Texas Chain Saw Massacre. Desperation and survival set against a vast sea of grass. A hole. A demon mask. A weird erotic charge. Some days, this is my favorite Japanese film.
Black Rain (1989, directed by Shohei Imamura) depicts the bombing of Hiroshima in one of the most harrowing sequences in any film about the war that I can remember. But Imamura frontloads the film with that imagery in order to get it out of the way (and to influence) the more subdued horrors that awaited the survivors. I'm not talking about the immediate aftermath, but rather the long term effects. In this respect it becomes one of the director's more subtle examinations of class and women in post-war Japan.
The Human Condition (1959-1961, directed by Masaki Kobayashi). Another war film, this time a three part epic about the war in Manchuria, and a complete and utter rejection of Japan's militaristic past. One can sense a deep personal investment in this movie from Kobayashi, who really hit his stride with this movie.
Goyokin (1969, directed by Hideo Gosha) is an anti-samurai movie. Oh, it's got enough action and enough "cool" to satisfy the most jaded chambara fan, but it's a negation of the Bushido code and the corrupt social structures it gave rise to. If Kurosawa was the John Ford of the samurai film, Gosha was the Robert Aldrich.
The Story of a Prostitute (1965, directed by Seijun Suzuki) was made for a pittance compared with the commercial films Suzuki was making at the time, shot on standing sets with very little budget. But this is my favorite of Suzuki's movies, one where, for a change, the director seems personally invested in the story, without throwing out his restless experimentation with film as an abstraction. Another film set in Manchuria during the war. It haunts a lot of the Japanese movies from this period.
Cure (1997, directed by Kiyoshi Kurosawa) is one of the creepiest movies I can remember seeing. For some reason, this film always strikes me as a way of processing the sarin nerve gas attacks in the Tokyo subway by Aum Shinrikyo, even though it really has absolutely nothing to do with it. A serial killer/police procedural, this veers off into Kurosawa's now-trademarked horror of ambiguous alienation in its second half. The creepiest of the new wave of Japanese horror movies.
A Snake of June (2002, directed by Shinya Tsukamoto) is a combination of pink film and film noir, filtered through director Tsukamoto's freak-out sensibility. This is comparatively restrained for him after the fireworks of Tetsuo, but I like that about it. An amazing addition to the cinema of voyeurism and sadomasochism, all filmed with a persistent veneer of oceanic dread. Yet surprisingly optimistic in the end.
Giants and Toys (1958, directed by Yasuzo Masumura) is a candy colored dismantling of Japanese corporate culture that seduces with the visuals before sticking the knife in. At its core, this is as nasty a film as American films like The Apartment or Sweet Smell of Success, but it goes them one further by radically breaking with the "rules" of Japanese cinema. This is edited fast, with its beats coming almost syllable for syllable sometimes. Nagisha Oshima exempted Masumura from his blanket condemnation of traditional Japanese film. This movie is one of the reasons why.
Odd Obsession (1959, directed by Kon Ichikawa) is my favorite of Ichikawa's many films, mainly because it demonstrates that even in 1959, the Japanese had a more incisive insight into the sexual relationships between men and women than could be found in any other national cinema. Nobody does weird psychodrama like them. This makes a great double feature with Masumura's Manji, which also adapts a novel by Junichiro Tanizaki.
Female Convict Scorpion: Jailhouse 41 (1972, directed by Shinya Ito) is the masterpiece of Japanese exploitation cinema. What you might get if you hired Mario Bava to remake Caged Heat. It doesn't "transcend" it's generic roots, so much as it sinks into them so deeply that they become a kind of abstract art. Meiko Kaji cemented her place as the queen of Japanese cult cinema in this series (of which, this is the second and weirdest). She doesn't speak much, but her lacerating stares speak volumes.
Pale Flower (1964, directed by Masahiro Shinoda), which finds the innovations of the Japanese new wave finding their way into genre films. This is an austere, chilly fall from grace in the tradition of the bleakest of film noir, laid bare with a staccato editing scheme. Shinoda later turned into kind of a mannerist, but in this film, he shows an instinct for the jugular.
And two animated movies:
Grave of the Fireflies (1988, directed by Isao Takahata), which is, bar none, the saddest film ever made. Reduces me to a puddle every time I see it, which isn't often because I don't think I could take it.
Steamboy (2004, directed by Katsuhiro Otomo) has all the eyedrugging destruction you could ask for in a steampunk epic, while never losing sight of the "fun" quotient. I like this a lot more than Otomo's groundbreaking Akira, but I'm generally not an enthusiast for Japanese animation, so take that however you like.