There were many reasons why Pluto got demoted to dwarf planet status, one of which was that it couldn't clear its orbit of asteroids and other debris. But Earth's orbit is also crowded...too crowded for Earth to be a planet?
Earth is indeed in a very crowded orbit, surrounded by tens of thousands of asteroids and other objects. As it turns out, that clutter still isn't remotely enough to cost Earth its planet status, but it's worth understanding just what makes Earth's case different from Pluto's. And to do that, we have to go back to the definition of a planet.
When the International Astronomical Union redefined the term "planet" in 2006, they agreed on three crucial criteria for planet status. The body had to orbit the Sun, it had to be massive enough to assume hydrostatic equilibrium, which essentially means it's big enough to be nearly spherical, and it had to "clear the neighborhood" that made up its orbit. It was this third criterion that Pluto failed to meet, because its orbit is right in the middle of the Kuiper Belt, full of planetesimals, asteroids, and various other pieces of debris.
That seems simple enough but, as always, the devil is in the details. As Ray Villard over at Discovery News points out, Earth is surrounded by so-called Near-Earth Asteroids. The prototype telescope Pan-STARRS (Panoramic Survey Telescope & Rapid Response System), located in Hawaii, can detect more than a dozen new asteroids on any given night, and some estimates tab as many as 20,000 asteroids in the same orbit as Earth.
The presence of so many asteroids seems like a serious problem for Earth's claim that it has cleared its neighborhood. And Earth isn't alone in this problem - Jupiter is surrounded by some 100,000 Trojan asteroid, and there's similar clutter around Mars and Neptune. Indeed, one object that Neptune has categorically failed to clear from its orbit is Pluto itself. Alan Stern, the head of NASA's New Horizons mission to Pluto and a critic of the Pluto reclassification, points out quite simply, "If Neptune had cleared its zone, Pluto wouldn't be there."
This seems like an untenable situation. After all, what sensible definition for a planet would exclude the largest in our solar system (Jupiter), the third-largest (Neptune), and, in Earth, the biggest rocky planet...not to mention the only one to support life?
Thankfully, there's a very simple way out of this. We've been talking a lot about the sheer number of objects around Earth and Jupiter, but let's instead consider those objects relative to the planets themselves. Pluto, for instance, is just .077 times the mass of all the other objects in its orbit, meaning it makes up roughly 8% of the mass found in its orbit. Earth, on the other hand, is 1.7 million times the mass of all the other objects in its orbit. Earth may be cluttered, but all the asteroids around it amount to less than nothing.
This figure is known as the planetary discriminant, an idea put forward by astrophysicist Steven Soter as a simple way of measure just how clean a planet's orbital neighborhood really is. As it turns out, Earth has the cleanest neighborhood of any planet, with Venus the closest behind with 1.35 million. Jupiter is the next cleanest, with a planetary discriminant of 625,000. As it happens, Neptune has the smallest discriminant, at just 24,000.
Even so, the difference in the size of discriminants between the eight planets and the five dwarf planets is massive. None of the dwarf planets - which currently includes Ceres, Eris, Pluto, Makemake, and Haumea - have discriminants greater than 1. The asteroid belt object Ceres has the largest, at .33, but that really is nothing compared to those of the eight planets. So then, Earth is definitely a planet, and the argument for its demotion rather resoundingly falls apart.
The IAU didn't include a strict cut-off for how clean a neighborhood has to be for an object to be considered a planet. Obviously, when the gap between the least clean planet and the cleanest dwarf planet is separated by a factor of more than 72,000, there isn't much need for one. So, barring the discovery of something very unusual in the outer reaches of our solar system (like, for the sake of argument, the Oort Cloud planet Tyche) that would seriously blur the line in terms of what it means to clear one's orbit, we can safely say that Earth is definitely a planet, Pluto is definitely a dwarf planet, and only one of them is capable of keeping its neighborhood clean.