There is no need to get concerned (astronomers consider the Moon to be "close") and this will rock will be pass us almost half again as far away.
Astronomers may get a bit excited as it should be visible in modest sized telescopes (more than 6" apertures). It will pass west to east through the pointer stars of the Big Dipper. Sky and Telescope prepared a chart, here (the times are in UT 5 hours ahead of us). At magnitude 10.5, you would need to know more exactly where to look for it.
For more information see the NASA/JPL page on this rock, here.
And just so you don't get surprised, there are some alarming views being fired around the Internet based on a video claiming massive electrical disruption. It's complete bunk and a good astronomy site called BadAstrononmy.com has a video debunking these claims, here.
It is important to keep looking for these rocks because if we detect them early enough, we can do something about them. It's just important to understand that "near" misses are much more common than most people think.
Astronomers are conducting organized searches to find and track Near Earth Objects. A list of frequently asked questions can be found, here. The most recent results of these studies are published, here. Wikipedia maintains a list of notable asteroids, including record close passes, here, and there is an article on very near miss known as the Great Daylight Fireball of 1972, here.
- Tu24 missed Earth as predicted. There is an article on what we should learn from it, as well as what we can do about these, here.
- WD5 is believed to have missed Mars and is now "lost" because its trajectory would have been altered by its close approach to Mars. See here. Also the Hubble was supposed to be taking pictures of it but I haven't heard of any being published yet. See here.
- Another small fast rock called 2008 CT1 missed us on February 5th by 133,000 km (well inside the Moon's orbit). This is a 10m diameter rock that would have created a nice fireball like the one in 1972. See here.
A massive explosion over Siberia in 1908 and known as the Tunguska Event is believed to have been caused by a large meteoroid or small asteroid.
Update 2008-2-10: I found a good write up on 2008 CT1, here. It orbits the Sun every 307 days and crosses the orbits of Mercury, Venus, and Mars. It is expected to come very close to Earth again in 2041 and 2060.