Physically (from an exterior and interior view of a person), cars will almost certainly continue to look just like they currently do - there seems to be no impetus to make radical changes in the actual appearance of cars.
However, there are some fairly radical changes coming to the construction and design of the actual car as a vehicle. Here are some of them which are currently in the prototype stage, and which likely will become commonplace by mid-century or so (2050 at the latest):
- Conversion of all cars to electric drive. For economy and efficiency's sake, it is highly likely that all cars will use electric engines in the near future (within 20 years or so). The big unknown right now is what power source will supply the electricity for the electric motor to turn the wheels. You may have gasoline/petrol/diesel combustion engines (as with the Chevy Volt) acting as generators, or you may have some sort of battery or fuel cell. Or perhaps some other mechanism. However, where-ever the electricity is coming from, the actual motive force turning the wheels will be an electric motor.
- Self-driving vehicles will be slowly phased in, and likely to be mandatory within 50 years at the latest. We are slowly adding advanced computer-controlled driving features (think ABS, traction control, and cruise control as the first wave) to cars, and are rapidly approaching the point where a fully-computerized driver is possible in a "normal" environment. See the DARPA Grand Challenge program for one which hopes to have automated driving in military vehicles by 2020. Civilian adoption will be more piecemeal, but I strongly predict that by 2050, all cars will come with a self-driving option, and soon after, laws will require that cars be self-driving.
- Change in methods of constructing a car's passenger safety cage. The current "unibody" construction is vastly superior in crash protection than the older "body-on-frame" concept. However, there are new ideas now around creating what is called a "floating cage" concept - think of the passenger compartment which is only loosely attached to the frame/body of the vehicle. The body can then crumple to absorb impact, while the floating cage can remain more rigid for protection.
- Inter-car communications will start appearing. In part with the adoption of computer drivers, cars will soon automatically communicate between themselves, sending road and traffic conditions updates amongst themselves. This will lead to far better road travel, as vehicles can automatically adjust speed and spacing according to knowing road conditions many miles ahead.
- Possible replacement of the standard "steel-belted radial" tire with a completely new concept. There are several newer tire designs vie-ing to be the new standard (the SBR tire design is now over 50 years old), which will increase tire durability, safety, and fuel efficiency.
- In the most radical visible change, cars will likely have their interior layouts completely revolutionized once full electric drives and automatic driving become standard. It will now be possible to build a car with an interior layout like, say, a limo (benches on the sides, or facing each other), or with re-configurable interiors.
- Changes in the construction materials, away from steel and/or aluminum to composites and plastics, are coming soon. Right now, these alternate materials are solely used for cosmetic purposes, or at best as body panels. Frame construction is exclusively steel. Advances in ceramics and composites are mean that strength can be had for less cost and weight - you should start to see significant use of both for structural purposes starting in the 2020s.
Most likely, a car from 2050 will look (to the viewer) almost identical to the one being made today in 2010. However, it will be a completely different creature, in the same way that a car of 2010 looks like, but is built radically different, a car from 1950. Cars of 2100 may finally start to look considerably different than today's cars, but that's much less certain.
Sorry, for a large variety of reasons, cars using air-cushion (hovercraft) suspension and flying cars aren't ever going to be possible in anything but the movies and as curious prototypes (or as playthings of the super-rich). Movement to different configurations (three-wheeled cars, 6-wheeled cars, etc.) are also unlikely to ever exist in more than microscopic numbers.