Actually, the kind of bike you're looking for is just called a folder!
These days there are 2 basic types of folders, commuter and military. Ironically, I would say the military is better for commuting, and the commuter is better for leisure. Both are often more expensive than your average bike because of design. Both would also take up very little room in your car.
The military bike folds out to almost the size of a standard mountain bike, but was designed to be carried by paratroopers so you can imagine how small they fold. Since they're almost the size of a mountain bike, it's pretty comfortable and you have room to stretch out your legs and can pick up good speed. Montague is the largest manufacturer of those bikes.
The commuter bikes are much smaller, so they pack even better than the military folders, but their wheels are tiny. They ride more like upright BMXes and are terrible for your knees. They're great if you're not tackling more than 2 miles a day on them. Dahon specializes in them, but I'd actually recommend the KHS F20. It's a really sturdy folder and a lot of the cheaper ones tend to have joints that fail (IE won't fold in the future).
Dahon also makes hybrid bikes that can fold, but they get pricey.