Which of the following definitions do you like?
Definition 1
A planet is a celestial body that
- has sufficient mass for its self-gravity to overcome rigid body
forces so that it assumes a hydrostatic equilibrium (nearly round)
shape, and
- is in orbit around a star, and is neither a star nor a satellite
of a planet.
This means there would be 12 planets in our solar system:
Mercury, Venus, Earth, Mars, Ceres (currently an asteroid), Jupiter,
Saturn, Uranus, Neptune, Pluto, Charon and 2003 UB313 (in the Kuiper Belt
of debris in the outer parts of our solar system). Those beyond Neptune's
orbit would be called Plutons.
See http://www.iau2006.org/mirror/www.iau.org/iau0601/iau0601_release.html
Definition 2
- A classical "planet" is a celestial body that (a) is in orbit around the
Sun, (b) has sufficient mass for its self-gravity to overcome rigid
body forces so that it assumes a hydrostatic equilibrium (nearly
round) shape, and (c) has cleared the neighbourhood around its orbit.
- A "dwarf planet" is a celestial body that (a) is in orbit around
the Sun, (b) has sufficient mass for its self-gravity to overcome
rigid body forces so that it assumes a hydrostatic equilibrium (nearly
round) shape2, (c) has not cleared the neighbourhood around its orbit,
and (d) is not a satellite.
- All other objects3, except satellites, orbiting the Sun shall be
referred to collectively as "Small Solar System Bodies".
This means that there would be 8 planets: Mercury, Venus, Earth, Mars,
Jupiter, Saturn, Uranus, and Neptune.
See http://www.iau2006.org/mirror/www.iau.org/iau0602/index.html
What Astronomers and Planetary Scientists Think
Check out this statement by the
Division of Planetary Scientists.