Nuclear cars will become the norm, and will pretty much dominate every other variety by around 2077.
I really hope you are joking
Okay, here is why we will NEVER use nuclear power for transportation.
1: Nuclear Energy is NOT clean, it may not produce carbon monoxide or dioxide, are other harmful substances, but nuclear power runs of a core of a radiactive metal (usually uranium 238 I believe). And the core gets extremely hot, so how does it cool itself? Well none other than water. The water that is used to cool the reactor becomes irradiated.
Irradiated water is extremely toxic (more than the pollutants caused from hydrocarbons)
2: What would happen if a car wreck occured? Their is the small potential for a nuclear reaction (ei: nuclear bomb) Although it would take some extreme cases that could probably be easily engineered around, it is still a liability. I would rather live in a world with melted snowcaps than a world with nuclear fallout.
3: Nuclear energy is expensive. The amount of safety and precautions that would have to be taken to make it safe for vehicle use is way different than its counterparts stuck safely in a reactor chamber in a nuclear plant.
4: Cars would become way heavier with the need to create the reactor. The main reason is because you would either need a thick layer of lead or concrete or some other dense material to prevent the deadly radiation from escaping the chamber
5: Its a HUGE liability trusting everyone with a stick of radioactive metal. Terrorists would have easy access to nuclear weapons from simply chopshopping a car and taking out the core and then packing it into a bomb shell with some other stuff.
I think the new source of fuel for our future cars will probably a breakthrough with either solar energy or a hydrogen-based energy source. I read something a while back out solar energy and how they have pathetic efficiency and with a breakthrough in the technology we could easily power the entire planet from solar power.
In the meantime before either of those happen, I'm guessing biodiesel. I don't like it one bit, but I think it's the most likely. And your probably thinking, "Why don't you like biodiesel? It's a renewable source and way cleaner than fossil fuels!" Because biodiesel is made from foods that humans commonly consume, if we began a large scale production of biodiesel food prices would soar, unless we created hundreds of millions of acres of farmland devoted to the production of biodiesel.
That's my two-cents