There are a number of alternatives - each with it's own particular difficulty.
You could use biofuels - diesel made from crops but there's not enough arable land to grow enough crops for our needs with existing crops. It might be possible to genetically engineer a crop like a fungus that could be grown fast enough but that's a way off yet.
Electric power - this suffers from 2 problems, firstly you have to generate the electricity in the first place and secondly battery technology's not up to the job, the range is limited to at best a couple of hundred miles with even the lightest vehicles before you have to recharge which is slow.
Personally I think hydrogen burning is the best alternative. You still have to generate the electricity to make the hydrogen but refueling is much easier and it's a very powerful fuel - a bit too powerful perhaps three are a number of safety issues about driving around with a fuel tank of explosive hydrogen gas.
Hydrogen fuel cells are another possibility but you're dragging around heavy electric motors and fuel cells and still have the hydrogen safety issues.