First you need to know how to make a rideable pig:
summon Pig ~ ~1 ~-1 {Saddle:1}

Then you should name the pig "Car":
summon Pig ~ ~1 ~-1 {Saddle:1,CustomName:"Car",CustomNameVisible:1}

Now make the pig invisible forever:
summon Pig ~ ~1 ~-1 {Saddle:1,CustomName:"Car",CustomNameVisible:1,ActiveEffects:[{Id:14,Amplifier:127,Duration:32167,Ambient:1}]}

The invisible pig has to ride a minecart:
summon Pig ~ ~1 ~-1 {Saddle:1,CustomName:"Car",CustomNameVisible:1,ActiveEffects:[{Id:14,Amplifier:127,Duration:32167,Ambient:1}],Riding:{id:MinecartRideable}

Now name the minecart "Car" too:
summon Pig ~ ~1 ~-1 {Saddle:1,CustomName:"Car",CustomNameVisible:1,ActiveEffects:[{Id:14,Amplifier:127,Duration:32167,Ambient:1}],Riding:{id:MinecartRideable,CustomName:"Car",CustomNameVisible:1}}

Now all you need to do is give the minecart a swiftness effect:
summon Pig ~ ~1 ~-1 {Saddle:1,CustomName:"Car",CustomNameVisible:1,ActiveEffects:[{Id:14,Amplifier:127,Duration:32167,Ambient:1}],Riding:{id:MinecartRideable,CustomName:"Car",CustomNameVisible:1,ActiveEffects:[{Id:1,Amplifier:5,Duration:32167,Ambient:1}]}}

NEW VERSION:

/summon MinecartRideable ~2 ~ ~ {Riding:{id:MinecartFurnace}}

NOTE: Only works on rails.

With this new, more compact version, you can control your speed when driving.
Simply hold S to speed up and W to slow down.
If you hold W too long you will end up in reverse.