Nippon Parking Development is offering one of the first car sharing schemes I've come across which might develop into an alternative to traditional car rental services for some Tokyo dwellers. It's called Ecoloca and the link will take you to the official site. I can't vouch for it, and I don't know how the costs look compared with renting, but I thought it was worth bringing up because I have friends who use similar schemes in Europe. The map on the site shows a limited number of pick-up locations centred on Shibuya and Aoyama so the service is in the very early stages.
The joining fee is 5,250 for an individual membership (which can include two people) or 10,500 yen for a group (which can include five people). If you join before the end of October then this fee will be waived. To get access to a car, you'll need an IC card and you will be charged 1,480 yen for one of these. There are then two different payment plans. Under Plan A, you pay a monthly 2,980 (3,980 for a group) and then a car rental fee of 160 yen for 15 minutes. Under Plan B, there's no monthly charge but 15 minutes will cost 260 yen. There's also a travel charge of 20 yen a kilometre and a "night pack" supplement of 3,500 yen. Fuel and insurance costs are included which is one of the major selling points of such schemes.
Available cars are currently the Nissan March (also known as the Micra), Mitsubishi Colt, and Nissan Wingroad while there are plans to add the Toyota Prius.