That is the question posed in this provocative article.
An interesting point in the article is that we never can run out of oil. Not in terms of having no physical oil available to extract-- the economics won't allow it.
The price of oil would rise as the quantities became more scarce. At some point, oil no longer becomes cost effective. This point is long before we actually run out.
Those of you have read Moby Dick might know that whale oil prices began to rise a great deal as whales were hunted to historic scarcity. Along comes Rockefeller and his cheap kerosene illuminant and the market for whale oil implodes. No one wanted whale oil any longer, and this was long before people were actually concerned about whaled becoming extinct.
Scarcity drives up price. The higher price prevents complete scarcity. At least for something that is as valuable as energy.
We will never run out of energy. The only question is what forms we will be using, and at what cost.