For the tl;dr crowd, let's get this out of the way right away: asteroid 2012 DA14 is almost certainly not going to hit the Earth next February. And by "almost certainly", I mean it: the odds of an impact are so low they are essentially zero. This does not rule out an impact at some future date, but for now we're safe.
So what's the story?
A small near-Earth asteroid was discovered in late February by astronomers at the Observatorio Astronómico de La Sagra in Spain, less than two weeks ago. Designated 2012 DA14, it's estimated to be about 45 meters (150 feet) in diameter, and has an orbit that is similar to Earth's.
Its orbit is an inclined ellipse, tilted a bit compared to Earth's orbit around the Sun (the positions of Earth and DA14 are shown for August of 2012 -- I picked that randomly to make the orbits clear), and it spends most of its time well away from our planet. However, the path of the rock does bring it somewhat close to the Earth twice per orbit, or about every six months. The last time it passed us was on February 16 - two weeks ago -- when it was about 2.5 million km (1.5 million miles) away, equal to about 6 times the distance to the Moon. That's usually about the scale of these encounters -- it misses us by quite a margin.
February 2013: a close shave
Next year, on February 15, 2013, DA14 will actually get pretty close to Earth. It will pass us at a distance of about 27,000 km (17,000 miles) -- well beneath many of our own orbiting satellites! To the best of my knowledge, this is the closest pass of a decent-sized asteroid ever seen before the actual pass itself.
However, let's again be very clear: it will miss. In astronomical terms, 27,000 km is pretty close, but in real human terms it's a clean miss.
[UPDATE: The rt.com article I linked below has changed substantively since I posted my own article here. They have attributed their quotations more clearly, and have taken out most of the more breathless rhetoric. I applaud them for doing so, though I wish they had been more clear in the first place.]
Unsurprisingly, though very irritatingly, I've seen a lot of websites writing about this as if the asteroid will hit. For example, rt.com has a very confused article about DA14 claiming it will somehow both miss us and hit us:
The rock's closest approach to the planet is scheduled for February 15, 2013, when the distance between the planet and space wanderer will be under 27,000 km (16,700 miles). [...] With the asteroid zooming that low, it will be too late to do anything with it besides trying to predict its final destination and the consequences of impact.
Blechh. They write that in a way to make an impact seem likely, but that's not the case at all! I've seen several other websites making similarly contradictory or confused claims (Note:I originally included this SFBay article as an example. It's not confused, but by using the phrase "potentially fateful day" it struck me as exaggerating the fear). The rt.com article even comes right out and says "NASA confirms... [DA14] has a good chance of colliding with Earth". This is simply not true. I'll note they don't actually give a reference to that, so it's not clear who, if anyone, actually said that, or where they got that information. Either way, it's wrong.
The fuzzy future
So we're safe for now. But what about future passes?
That's harder to say. Predicting where an asteroid will be at some future time depends on a lot of things, including how good the observations are now and how long we've been watching it. When we observe an asteroid with a telescope, we can measure its position, but not with perfect accuracy. The Earth's atmosphere blurs the image a bit, and other factors make it impossible to get an exact measurement. So we observe it many times, over as long a period as possible, to hammer down those uncertainties.
There will always be some small amount of fuzziness to the orbit of an asteroid, though, and the farther ahead in the future you look the bigger that fuzziness gets. For next year, we know the orbit of DA14 well enough to know it'll miss, but for future orbits it's harder to say.
As things stand, right now the JPL website lists the next close pass as February 2020, but we don't know the orbit well enough at this moment to know how close that pass will be*. As things stand, the odds of an impact even then are very, very low (like, 1 in 100,000 -- less than your odds of getting hit by lightning in your lifetime). We can't technically rule it out just yet because, again, the orbit isn't known well enough to look that far into the future. Of course, astronomers are observing the asteroid right now, and will continue to do so. No doubt we'll have better orbital information pretty soon.
Keep watching the skies!
So again, because I can't say this strongly enough: asteroid 2012 DA14 is not an impact threat for February 2013. However, we definitely need to keep our eyes on this guy to see if it poses a threat at some future date. If it does, then you can be sure you'll be hearing about it from me, and from other websites too. But make sure you find reliable websites. Too many are too ready to breathlessly report this as doomsday when it's anything but.
So, at least for February 2013, we can safely say:
* I'll note the European NEO-DyS group uses different mathematical techniques, and they don't even list that date as a near pass. Instead, they say it'll be six months later, in September. Again, this shows that given our current observations of DA14, predicting its position that far in the future is very uncertain.