It is much less likely that we're hit by a really big asteroid now than it was several billion years ago. In the early days of the solar system, while the planets were forming, there were many more asteroids flying around (makes sense, given that this is how planets form and grow - by accreting lots of planetesimals). So you start off with lots and lots of small bodies, and then towards the end of the process, you're left with fewer small bodies and some large ones. One of the large (Mars-sized) objects hit Earth a glancing blow about 4 billion years ago and the Moon formed as a result of that.
So the impact rate was high about 4 billion years ago - even after the planets formed, there was a lot of debris still flying around - but eventually most of the big and small bodies in the planet-crossing orbits would have either hit the planets or been flung out of the system or into "safe" orbits. So the impact rate dropped, and has been very slowly dropping ever since. But the risk is always there - after all, we got nailed by a small (km-sized) rock about 65 million years which wiped out the dinosaurs and much of the rest of life on Earth.
In more recent years, in 1908 we got hit by a very small rocky object that blew up in the sky over Tunguska, Siberia with the force of a small nuke. In 1994, we saw a comet broken into many pieces and hit Jupiter - if that happened on Earth, we wouldn't have a chance. The risk of impact is still very real - but governments don't seem to want to do much about it. While it is very unlikely, fact is, if it does happen we're toast. It just takes one smallish rock to hit Earth to end civilisation.