According to Wikipedia, these are the IAU criteria for naming a body of the solar system a planet:
"The definition of planet set in Prague in 2006 by the International Astronomical Union (IAU) states that, in the Solar System, a planet is a celestial body which:
is in orbit around the Sun,
has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and
has "cleared the neighbourhood" around its orbit.
A non-satellite body fulfilling only the first two of these criteria is classified as a "dwarf planet". According to the IAU, "planets and dwarf planets are two distinct classes of objects". A non-satellite body fulfilling only the first criterion is termed a "small Solar System body" (SSSB). Initial drafts planned to include dwarf planets as a subcategory of planets, but because this could potentially have led to the addition of several dozens of planets into the Solar System, this draft was eventually dropped. The definition was a controversial one and has drawn both support and criticism from different astronomers, but has remained in use.
According to this definition, there are eight planets in the Solar System. The definition distinguishes planets from smaller bodies and is not useful outside the Solar System, where smaller bodies cannot be found yet. Extrasolar planets, or exoplanets, are covered separately under a complementary 2003 draft guideline for the definition of planets, which distinguishes them from dwarf stars, which are larger."
The Wikipedia article on the evils of Pluto is interesting.