Oil becomes more expensive to extract as it becomes harder to find. So, if oil were to become scarce, the price would slowly creep up, driving innovation and investment into alternative energy sources. Oil is popular because it's cheap. If it became expensive, it would be too valuable to burn as fuel, and the only users would be industrial manufacturers, who use petroleum to make chemicals used in plastics and other synthetics, as well as fertilizers and such.
There is good evidence that at some point, oil deposits will begin regenerating at a faster rate in deep locations. This is because there is more than one way for oil to be created... it's not just dead plants and compressed dead dinosaurs. The evidence for this is still being evaluated, but it would imply that oil is not necessarily a completely non-renewable resource.