The short answer is 'no'.
There are absolutely huge quantities of fossil fuels on our planet. We certainly won't run out of oil for the foreseeable future and certainly not for hundreds of years at least. The problem is that people often confuse the estimated quantity of fossil fuels on the planet (massive!) with the amount left in the deposits we're currently mining, pumping, drilling, etc (dwindling!).
We, as a species, started by extracting the fossil fuels that were easy to get to. Obviously, as time goes on, these 'easily accessible' fossil fuels will dry up. That means if we want to continue to use fossil fuels we have to go looking for 'not so easily accessible deposits'. This is why you have oil companies doing deep sea drilling and countries like Russia placing little flags under the polar icecap in ridiculous attempts to 'claim' new regions.
So fossil fuels are far from 'running out' but that's not the issue. The real issue is that, as we try to remove fossil fuels from the 'not so easily accessible deposits', they become more expensive. These deposits tend to be in and around countries that are notorious hot spots of geopolitical problems - a regime change in Libya, for example, shifts oil prices globally and everyone ends up paying more. We've already seen situations where some countries, like Russia, simply switched off gas supplies to other nations.
The reasons why we need to shift away from fossil fuels have very little to do with the quantities left in the ground. The main reasons are due to the volatility of the market and constantly fluctuating prices, the lack of security in having other nations supplying energy (and therefore being dependent on what happens in those nations), the environmental consequences of having to access fossil fuels from 'not so easily accessible deposits', and the unrest that will undoubtedly occur when western nations spend large sums buying up fossil fuels leaving poorer nations without.
At the moment we have no viable alternative that can match fossil fuel energy production. Wind, solar, tidal, etc are all useful but are variable and output changes depending on the day. Nuclear is one option but we've long passed the deadline to be able to build enough new reactors for the task. Fusion is the only real long-term option but we consistently invest paltry sums of cash into the research relative to the potential - the ITER reactor in France is going to cost about 15 - 20 billion euro. To put this into perspective, the Manhatten project cost the modern equivalent of about 24 billion dollars and the Apollo missions about 170 billion in 2005 dollars.