You've probably heard the news a few days ago that astronomers came up with a new definition for "planets" that added 3 new planets to the solar system (including the largest asteroid, Ceres). A couple days ago, another definition was proposed, which appears to be more consistent in some ways. However, it excludes the farthest traditional planet, Pluto. By and large, professional astronomers don't care too much one way or the other -- reactions like this (Rob Knop) and this (Phil Plait) are pretty typical. In general, what a "planet" is matters more to the general public than to the pros.
Even given that, you do have to wonder what the fuss is about. It's pretty clear nowadays that Pluto is a very small object, different from the other 8 traditional planets. In fact, Pluto is more like the largest non-planetary bodies in some ways. Pluto is about a dozen times more massive than the largest asteroid (Ceres), but the smallest remaining planet, Mercury, is more than 20 times more massive than Pluto. Seven satellites (our Moon, the four large moons of Jupiter, Saturn's moon Titan, and Neptune's moon Triton) have more mass than Pluto. If Pluto had been discovered yesterday, or even 20 years ago, rather than almost a century ago, it almost certainly would not have been called a planet at all!
So why was Pluto ever considered a planet in the first place, rather than something like a really large, icy asteroid? It turns out there is a lot of interesting history behind this, involving a couple of great planet hunts in past centuries. More below.