We've not seen any proof that oil is finite. As time progresses new technologies enable us to get at more oil every year. "Peak oil" was supposed to happen twenty years ago, yet new sources are still being discovered all the time.
But if prices continue to stay high the oil companies and oil exporting nations will eventually price themselves out of business. Twenty years ago the electric car was a joke, today there are several models available on dealer lots for purchase with more in development. We have also made great strides in fuel economy of traditionally powered vehicles, 40MPG is a reality many Americans see every day. Another 20 years may see 60MPG as a reality, with many vehicles using no gasoline at all on the daily commute.
If we get close to the $3/gal national average price again drilling in the US will become profitable once more. What OPEC and these Middle-Eastern nations don't understand, they're slowly pricing themselves out of business. On the bright side kicking oil to the curb will mean the Middle-East's influence on the global scale will drop dramatically... which is a very good thing.