The world? No, the planet will probably be around for another 3 billion years or so. At that point the Andromeda Galaxy is going to crash into the Milky Way and the two supermassive black holes at the center of each galaxy will spiral into one another, pulling in billions of stars and eventually colliding to form an even bigger black hole. The Earth will either be sucked into the black hole, or hurdled out of its orbit and out of the galaxy as supernovae strip away the atmosphere and boil the oceans off.

But in the near future, there is no reason to believe anything that catastrophic will happen. However, civilization as we know it may be coming to an end. What is certain is that in the next few decades the depletion of the world's petroleum supplies will drastically change the way we live our lives. The current agricultural and transportation networks will not be able to function without petroleum, since all commercial pesticides, fertilizers and modes of transportation are petroleum-based, and there is nowhere near enough time to convert even a significant portion of that to some alternative energy source (and even then, no known alternative energy sources are capable of doing what petroleum can do anywhere near as efficiently). And even if there were enough time, who's going to invest the humongous amounts of money?

http://www.oilempire.us/peakoil.html
http://www.lifeaftertheoilcrash.net/
http://www.hubbertpeak.com/
http://dieoff.org/