Rival Schools: United by Fate
This is probably the best 3d fighting game from Capcom to be released onto the Playstation. It has many over 20 characters and the number doubles because every single character you beat it with unlocks another. But that pales next to what you get in the Japanese version.
Sadly removed from the American release was the ability to create a character by going through a kind of school simulation. Most of the characters are high school students or teachers. The wildly popular Kyosuke (also in capcom vs. snk) is from Rival Schools. Sakura from Street Fighter appears in it as well. It has one of the best developed plots in a fighting game ever. Anime segments complete with Japanese voice acting are between every fight in story mode. Speaking of which, hearing Roy say "come on baby" is quite funny.
It also includes arcade mode, vs mode, tournament mode, and several mini games. This game is overflowing with style and is definately Japanese. Some of the minigames are downright scary. Checkout Kyoko's office to see what i'm talking about. The coolest feature of this game however, is the team up techniques. You choose two fighters for each fight and the second character can heal you, raise your special meter, or assist you in an attack. All the characters are extremely well animated, if not a little blocky. The cast is also very memorable thanks to the several different stories and endings for each. If you buy any 3d fighting game for the Playstation this is it, it has near infinite replay value. It is my favorite 3d fighter with the possible of exception of Rival Schools: Project Justice, for Dreamcast.