Electrolysis would do it, but as you say, its inefficient with water so it could never work well enough to power a car. 
 
But think, pure oxygen makes stuff burn very quick. 
 
Hydrogen is the most volatile/explosive/reactive substance around. 
 
Imagine hydrogen going off in pure oxygen... 
 
You'd get a scooter engine more powerful than a car. 
The plus side is, hydrogen + oxygen = water, so when you split the water, then ignite the products, you get more water, which is theoretically an infinite fuel source. 
 
  
Haha, you're a clever one! 
 
Yeah, it would be the same with the water if you could split it. You'd only have to top it up every once in a while 
 
Some electric cars are pretty quick nowadays.