Do you mean the destruction of the entire planet, or just life on the planet? Millions of years from now, the Earth will someday be destroyed when the Sun starts to run out of fuel. The Sun will expand--over millions of years. It will get so big that Mercury, Venus, and eventually Earth will touch the Sun's surface, collide, and be absorbed into the Sun. Then later, the Sun will shrink until it's a mere shell of itself, a white dwarf star, cold and dim.

Most of the life on the planet could be destroyed much sooner, by an asteroid, nuclear war, or other catastrophe. *Some* kind of "life" will almost certainly survive, but it might just be microbes, insects, and other small creatures for a while.

If you are talking strictly about the earth as a system, then, this has to do with climate changes, atmospheric changes and all the things that come with it (water levels rise, livable land is lost, air is no longer able to support life). Could this happen? Yes. Could it happen soon (under a 1,000years)? Probably not. Earth as a system tends to move in cycles. If you look through Earth's history there have been many different levels of oxygen and carbon dioxide in the atmosphere, temperatures have been much hotter(80degreesF average worldwide, average today is about 12degreesF) or colder(Earth about 3 billion years ago was one big ice sheet, also called a snowball Earth). If instead you are talking about Earth being destroyed by a meteor or asteroid, this has happened many times in the past and probably will happen again the future. Remember the Earth has been around for 4.6billion years and life has been around about 1.2 billion years. I personally think many people think negative and only think of the bad things that can happen. Wouldn't it be wonderful if all we heard in the news was about all the great teachers, musicians, artists, doctors, etc there were and what wonderful things they are doing, instead all we hear about is all the tragedies.

In approximately four billion years, the Sun will become a red giant, and will swallow the Earth whole.

Before then, the Earth is going to get cooked as the Sun *becomes* a red giant.

Aside from that, I can't think of any likely reason why the Earth would become sterile. We humans may by our behavior make it uninhabitable for us, but whatever we do, the cockroaches are going to outlive us.