So far, the Earth has experienced five notable mass extinctions. Scientists don't know the causes for all of them, but asteroid impacts probably made a contribution to at least two. One is the infamous Cretaceous-Tertiary extinction, which led to the end of land-walking dinosaurs. Other factors, including volcanic eruptions, likely played a role in that event as well.
Asteroids collide with the Earth all the time, but most burn up in the atmosphere. The bigger the asteroid, the bigger the threat — but the smaller the chance it will hit the planet. According to NASA, an asteroid big enough to seriously affect life on Earth collides with the planet once or twice per million years. NASA and other organizations are surveying the sky to find the locations of all near-Earth asteroids (NEAs) that might pose a threat to the planet.
According to New Scientist writer David Chandler, the biggest known threat is an asteroid called 1950 DA. This asteroid has a 1-in-600 chance of colliding with the Earth in 2880 — not in our lifetimes, but in the foreseeable future.