I can at least name the following alternative energy sources that all have been used to fuel cars: ethanol, biodiesel, biogas, natural gas, liquified petroleum gas, hydrogen, electricity.
Ethanol: ethanol has been used over century ago for fuel until gasoline derived from petroleum displaced it, so the technology is very mature and the fuel is not terribly expensive. The modifications needed to run on ethanol are in many cases rather small, possibly allowing converting a gasoline car to ethanol, but that won't allow full utilization of the high-octane properties. The best way to run on high ethanol mixtures is to buy a car that was originally designed to utilize high-octane fuels (high compression ratio), meaning you get more distance from a liter of ethanol. Ethanol is very beneficial as octane booster, mix 10% of it to gasoline and that's the cheapest way to make cheap gasoline high-octane without using any lead-based additives. 100% ethanol has poor starting properties in cold, which is why usually ethanol cars run on 85% ethanol + 15% gasoline. A problem is the low energy density, a liter of ethanol doesn't provide as much energy as gasoline, so you get less range even if the car has an engine that has been designed to run on very high octane fuels. A benefit of ethanol is that ethanol cars usually run on gasoline too, so you can always find fuel. A problem of ethanol is that we don't have enough capacity to produce enough of it to all cars without sacrificing carbon capture targets or food production. Burning ethanol releases carbon, and if the carbon was from biological sources, you could have captured it in solid form and stored it for the long term, so even though carbon-neutral, it displaces opportunities for carbon-negativity.
Biodiesel: there are two kinds of biodiesel, fatty acid methyl ester and hydrotreated vegetable oil. Fatty acid methyl ester is the older technology and isn't 100% compatible with fossil diesel so it may not work on some modern diesel cars, and even if it works, the engine longevity may be a concern. Hydrotreated vegetable oil is the newer kind promoted by Finnish company Neste. It should be 100% compatible with any diesel car even in 100% mixtures. Also a benefit of biodiesel is that cars running on biodiesel can also use regular diesel so you can always find fuel. A problem of biodiesel is that we don't have enough capacity to produce enough of it to all cars without sacrificing carbon capture targets or food production. Burning biodiesel releases carbon, and if the carbon was from biological sources, you could have captured it in solid form and stored it for the long term, so even though carbon-neutral, it displaces opportunities for carbon-negativity.
Biogas: Biogas is just like natural gas, i.e. methane, but from biological sources. A benefit is that if you can't find biogas, you may be able to find natural gas, so finding fuel doesn't require you to buy carbon-neutral fuel. A problem of biogas is that storage of compressed gas is difficult in large quantities (takes space and costs a lot), so usually the pressure vessel size is small. This means range is limited. This may be offset by a secondary gasoline tank allowing you to have more range. Another problem of biogas is that we don't have enough capacity to produce enough of it to all cars without sacrificing carbon capture targets. Burning biogas releases carbon, and if the carbon was from biological sources, you could have captured it in solid form and stored it for the long term, so even though carbon-neutral, it displaces opportunities for carbon-negativity.
Natural gas: natural gas has exactly the same properties as biogas but is from fossil sources. The benefits and drawbacks are the same, with the additional drawback that you are funding a certain maniac called
Vladimir Putin Vladolf Putler and contributing to climate change, both via leaks and via carbon dioxide. It's a fossil fuel so not carbon neutral. However, it's so little used it could be considered "alternative fuel", and also any natural gas car runs on biogas equally well, and biogas is not a fossil fuel.
Liquified petroleum gas: it's a very little used fuel consisting of propane and butane, with main problem being that oil production produces so little for it and there are better uses that exploit its advantages. An advantage is that it's a gas (so creating burners is easy) but liquifies easily (so you can store a lot of it in low pressure). Better uses for these fuels are barbecue grills, emergency cooking appliances and camping cooking appliances (propane, butane) and lighters (butane), that optimally require a gas that liquifies easily. I understand that in Kazakhstan, this is actually used as a fuel for cars. However, elsewhere, you can't find the cars or the fueling stations. There is no substitute for LPG, so if your car runs on LPG, you can't find an alternative with the same properties, so unless the car was designed as a dual fuel car, you may be out of luck. It's a fossil fuel so not carbon neutral. However, it's so little used it could be considered "alternative fuel".
Hydrogen: Hydrogen suffers today from the dirty production process from natural gas, which is very energy-inefficient and produces lots of carbon dioxide. Also if you today buy hydrogen, you are funding
Vladimir Putin Vladolf Putler indirectly via supporting the price of natural gas. However, it is almost certain that in the near future, in 10 years or so, electrolysis and electricity costs become so low that the cheapest source if hydrogen is electrolysis of green wind/solar electricity. The main benefit of that is it's a natural stabilizer for electricity grid. If there is enough wind and solar for most electricity being green, in maximum power production hours we have to find a use for the excess electricity and that's hydrogen. In large scale, hydrogen storage is cheap although 3x more expensive than that of natural gas -- it is stored underground. In small scale, storage is very expensive, because hydrogen has one third of the volumetric energy density of natural gas and it won't liquify unless very close to absolute zero. Another problem for hydrogen is that hydrogen engines are just silly and energy-inefficient in small scales (although in large scales hydrogen engines can compete with fuel cells) so practical small-scale usage requires fuel cells, and those are expensive as hell today and longevity isn't as good as it is for example for batteries. Even if fuel cell problem is stored and all hydrogen is produced from green electrolysis, hydrogen still suffers from being less energy-efficient than direct battery electricity. Today, finding fuel stations is practically impossible (if you find one you'll find the fuel cost is astronomical) and there are only few hard-to-obtain cars that run on hydrogen and those are very expensive to buy. This is expected to change, but most likely scenario is that hydrogen never catches up with electricity in passenger cars. However, large-scale trucks are a different matter, hydrogen is expected to win electricity in long-haul large-scale trucking. Hydrogen car runs only on hydrogen, there is no alternative fuel substitute for it. A benefit of hydrogen is that it is completely free of carbon and there exists a clear pathway for making green hydrogen. A drawback is that in small scale passenger cars, electricity probably wins.
Electricity: today, lithium ion batteries are cheap and can be made large enough that electric passenger cars are feasible. There is enough lithium to make all cars electric, cobalt may limit the production of some battery types but as lithium iron phosphate patents expire that will become the main battery type and it requires absolutely no cobalt or any other rare minerals (apart from lithium which we have enough). This is today by far the cheapest long-term cost option for passenger cars, and electricity produces no carbon after generation becomes based on renewables (we have a clear pathway for that -- based on wind/solar chiefly, plus hydrogen/hydropower/batteries for storage, plus some alternative pathways like nuclear power if some parts of the most likely pathway turn out to be difficult). A difficulty is that range is limited, recharging is slow even in optimal stations (from 30 minutes to an hour 10-80% charge) and most charging stations are even slower than that. Electric vehicles suffer when cold because only reasonable way to produce heat, heat pumps, uses electricity and the heat ain't free, and recharging when cold is slow as battery needs to be heated first which requires lots of energy and time. Also batteries are less efficient when cold. Furthermore, if you want to find a car with large enough battery that it's actually useful as a main car, you are limited to only some newest models that are very expensive even when used. By far, on basis of energy efficiency, battery electricity wins any other technology. It's also carbon neutral. A major problem is that this is the only energy source that's dependent on operation of the large-scale grid that can very easily become damaged for a period of months to years during a solar storm. Producing the electricity for charging by using a small-scale gasoline generator easily brings the total fuel consumption to 16-20 liters of gasoline per 100 km even for the most efficient electric cars.
Overall, it's a fact that only hydrogen and electricity are possible on the large scale. So that's what most of cars will be based on. Whether or not limited sales of other cars are permitted is up to the lawmakers to decide. It may be best to save the limited amounts of carbon-based biofuels we can produce sustainably for aviation for example.
Biodiesel (100% hydrotreated vegetable oil) is widely available in many refueling stations in Finland. Not sure about the status in other Europe, but I suspect it will become widely available there as well.
Cars can also be fueled by quite many fuels, for example methanol, but I suspect my list includes the main energy sources that are actually in use around the world today.