Although there are certain number of local car rental companies, most car rental companies located at airports are international brand such as Avis, Hertz, and Budget in Europe.
However, Japan is different. These major companies do not operate directly in Japan. On the other hand, Japan has its own car rental companies which have nationwide branches.
Japanese car rental companies can be divided into two groups. The first one is subsidiaries of automobile manufactures, such as Toyota and Nissan. The second one is independent companies such as Nippon Rent-A-Car and Orix Auto. Of course Toyota and Nissan use only their vehicles, therefore their offers can be limited than the independent companies.
JR groups also offer car rental service called Eki Rent-A-Car, which Eki means station in Japanese. Offices are located at almost all Shinkansen stations and other major stations throughout Japan, especially outside of Tokyo metropolitan area. JR also offer package including train tickets and car rental.
Biggest car rental market is Hokkaido and Okinawa. Hokkaido which is biggest prefecture in Japan is a place where you need a car when traveling due to less frequency of trains and poor railway network. Then, due to high season for traveling in Hokkaido is summer, car rental companies have special rates for Hokkaido especially in summer. Okinawa which has only 1 monorail line running within prefectural capital Naha, car is need to travel within the islands.
By the way, all vehicles belonging to car rental companies in Japan have to use hiragana わ(wa) or れ(re) on their vehicle registration plate, therefore it is very easy to recognize which vehicle is car rental or not.