Today we have diesel and petrol cars and a few hybrids, the most successful being Toyota Prius. As this industry is build on inoculation of the idea of having a personal vehicle, unless some catastrophic event (natural or economical) happens I don't see that many people giving up their beloved cars no matter how good the public transport will be.
So what will be the future of cars? Among the alternatives to oil based propelled cars the hype is nowadays on electric cars. Some estimates are saying that by 2020 10% of new sales will be electric cars, others estimate the adoption rate will be much slower to only 1-2% of new sales. At least one big company (Renault) is betting on the first estimate and plans to launch a full range of electric cars in a few years. The main drawbacks for electric cars at this moment are the cost of batteries (most of them use lithium which is not that abundant) and the infrastructure for recharging them. See the full story here.
As for myself, I hope the next car I buy will be at least a hybrid one.