Given that a vehicle could be powered by an electric motor, an internal combustion engine, or some form of external combustion engine (e.g. a steam engine), any chemical reaction that produces either an electrical output, heat, or gaseous pressure (e.g. two liquids reacting to create a gas) could theoretically be used to create the necessary motion. Similarly, any other means of producing electricity, which can be either stored in a battery or used to create a fuel (e.g. by electrolysing water to hydrogen and oxygen), could be used.
So solar, wind, geothermal, tidal, wave, hydro, nuclear power are all possible, along with biofuels such as biodiesel or ethanol. Current biofuels tend to be based on the same or similar crops as used for food or cooking (e.g. corn, rapeseed, sugarcane), but biofuels from algae and bacteria are also being researched.