There are always a lot of doomsday predictions about asteroids. NASA has us covered on this front, but paranoid internet bloggers might argue otherwise. The latest scuttlebutt has us all perishing in September. Regardless, there are a lot of near-earth objects. This graph of NASA’s database on NEOs between 1900 and 2200 shows that these visiting asteroids (and comets, but those don’t have a defined absolute magnitude, so they aren’t graphed) are actually pretty common, and many come even closer than the distance between Earth and the Moon.

Note there is some observational bias in these data; we know much more about the ones that are due to approach now-ish, or approached recently, and we can track much smaller objects that are near approach with higher certainty. So the shape of the trend is less significant than just the sheer volume. This database has more than 21k just out to a range of 30 lunar distances!

Data source: http://neo.jpl.nasa.gov/cgi-bin/neo_ca