Non-renewable energy sources are those where there is a limited, fixed supply that gets used up. They include the fossil fuels (Coal, Oil and Natural Gas) and, surprisingly, nuclear fission (used in nuclear power stations).
While it is possible to ask when will they run out, a better question is to ask when will they become scarce and expensive? The answers are complex, but can be summarised as follows
Geologists, analysts and oil companies disagree, but make claims for anywhere between next year and 30 years time. This is the peak oil debate.
Coal - there is enough coal to last several hundred years. Or is there?
Fission - MIT estimated in 2003 that, using current reactor designs, there is only enough usable uranium ore to power 1000 reactors for 40 years. New reactor designs may extend this considerably, but eventually the ore will run out.http://www.technologyreview.com/Energy/17059/page3/