Raist put it pretty well. There is no single problem, they are many. Poverty, ignorance, greed, politics, religion all these. Interestingly greed and poverty are linked closely, if we could spread the wealth more evenly it may eliminate problems.
Apathy is a big problem. If global warming is really going to end the planet then surely people would be doing a hell of a lot more to stop it, and by this I mean everyone. War and peace the same. Too many people don't care about terrorism, global warming, war in Africa etc as it may not directly concern them and they are probably more worried about meeting basic needs like getting dinner on the table and making sure the kids are tucked in bed (making ends meet).
A good example is the useslessness of foriegn aid and charities like World Famine. (Not that these are bad ideas, I really try support only support 3 charities.) Problem with these is if people cared enough to give enough, including governments, we would elimate a lot of problems. People either don't care to even support them or make minimal donations as most money goes towards supporting themselves.