Actually, you see, the internal combustion engine replaced the steam engine to power vehicles of all kinds. It was originally used in locomotives in the 1800s to connect the east cost of the US to the west coast. They also powered paddle wheel boats up the Mississippi and allowed for powered crossings of the Atlantic Ocean. But enough of the history lesson.
There are some inherent downfalls to using steam to power a car:
Startup Time - We are used to getting into a car, starting it up, and relatively quickly just going. In a steam powered vehicle, you have to warm up the boiler before you can start using it. It has to get warm enough to create steam in which will drive the engine. Depending on the model of steam engine, this could take an hour or longer to occur. There's no just jumping into the car and going to the store. There is a notable exception which was the Doble Steam Car which had a specific gas burner and small tubing which only contained a small amount of water at a give time. This allowed for the water to flash to super hot steam in short order. The start-up time on this was relatively short.
Big and Bulky - A steam engine usually weighed a lot. This was due to it being in two parts (water boiler & engine itself). It took a lot of metal to keep pressure contained so it could be usable. In this age of "smaller is better" format, having the bulk of a steam engine would make it obsolete before it ever got off the design canvas. You could never get the aerodynamics which are seen today on cars with internal combustion engines.
Dangerous - Unlike modern internal combustion engines, a steam engine was dangerous in comparison. You had a boiler which would get pressurized very high (especially considering the metallurgy of the day). This pressure is what drove the steam piston. Plus you had an external heat source (fire) which also posed dangers. If a boiler were to explode, not only would there be shrapnel from the boiler, but steam and boiling water would blow every where in a given radius, causing injury to any in the way.
Low Efficiency - It is stated that a steam engine only has a ~20% efficiency (not that this is too much different than a gasoline internal combustion engine).
One great thing which the steam engine had was you could produce gobs of torque with them. In the Doble Steam Car which was mentioned above, it had four pistons which powered it. With a steam engine, the piston could provide power on both the "up" and "down" strokes of the piston (this is a relative notion, as in this car the pistons lied flat to the ground). If you compare this to an internal combustion engine, you get power with each stroke of the engine, which means with the four cylinders, you'd have 16 power strokes for the four pistons over two revolutions of the crankshaft. With a gasoline 4-stroke engine, you'd only see four power strokes during the two revolutions of the crankshaft. This is a great advantage because along with the super heated steam, it provided upwards of a 1000 lb-ft of torque.