Like a rhinoceros lumbering across the savannah with a few oxpeckers as passengers, Earth is accompanied in its orbit by several diminutive followers known as co-orbital asteroids. They share the same region of space as Earth does, orbiting the Sun with nearly the same period, but they're entirely in Earth's thrall, their courses wholly dependent on Earth's comparatively gargantuan gravity. These orbits are not usually stable over the age of the solar system -- they'll hang out in our neighborhood for a little while, maybe some tens or hundreds of years, but sooner or later they'll wander out of this unstable equilibrium and get tossed out of Earth's neighborhood. Though not out of the solar system; I'm pretty sure that Jupiter is the only planet whose gravity packs enough oomph to eject bodies entirely out of the solar system.
Co-orbital asteroids are in the news right now because there is one called 2009 BD that has just passed extremely close to Earth, just a little farther than one lunar distance away from us. It's very small, about 10 meters in diameter, and was only discovered days ago (you can tell that from its name; 2009 is the year of discovery, and the first letter tells you which half-month it was discovered in -- "A" would be first half of January, but as it is "B," that means it was discovered during the second half of January). It poses no impact threat to Earth.
As I am going utterly crazy with my impending home move I don't have time to write a well-researched piece on 2009 BD but fortunately there are some people who've already done that, notably Astroprof and Ian O'Neill. If you want to look at 2009 BD's orbit and run it backward and forward in time to see how it moves with respect to Earth, you can play with the interactive Java orbit diagram thingy at JPL's Near Earth Objects site. If you let the time run, and consider how the object appears to be moving from the point of view of Earth, you can see that 2009 BD orbits in sort of a springy corkscrew around our orbit. Fun.