It's probably a little unfair to lump all the Japanese manufacturers together, but I don't claim to know a lot about them, especially their domestic racing, where sportscar racing is possibly the biggest form of motor racing.
Undoubtedly, the driving force in Japanese involvement in sportscar racing is a desire to win Le Mans.
There is a Japanese GT series website.
Mazda led the way in World Sportscar racing by bringing one of their rotary engined cars to Le Mans. They've since become a well established presence at Le Mans and are, to date, the only Japanese maker to take that much valued win. Mazda claim that showroom sales increased by 30% after their 1991 win; remarkable, if true.
Nissan have also been a frequent competitor at Le Mans and during the heydays of Group C. After dominating the IMSA series in the 80s, they moved over to the Group C series with a sleek, Lola built car, powered by an excellent V8 twin turbo engine. On many occassions the cars looked like outside bets for victory, but they proved a little fragile and the wins eluded them, both in the World Endurance Championship and at Le Mans.
In 1997, they returned to Sportscar racing in a big way with a TWR designed 'GT' powered by that Group C V8. In testing they were fast, but late changes to the cars (supposedly due to late clarification of the rules), led to gearbox problems, despite showing well in the early stages. Expect them back next year, but the cars seem unlikely to meet the FIA's GT regulations, so it may be that they only ever appear at Le Mans.
Like Nissan, Toyota were regular competitors in the Group C days, with their V8 powered cars. They also struggled onto the end of the Group C days with a 3.5 litre V10 engined car, which came close to winning Le Mans a couple of times, once against the Peugeots and once against the Dauer-Porsche 962 'GT' car.
They've also dabbled with a Supra in GT spec, but despite being highly competitive in the Japanese GT series, it proved overweight and ill-balanced at Le Mans. They are rumoured to be returning to Le Mans in 1998 with a 3 car GT challenge to Nissan.
Unlike the other manufacturers, Honda have concentrated on F1 for their motor racing campaigns. However, they have run NSXs at Le Mans on a number of occasions, but despite good reliability, they've been too slow to make any real impact on the race.