The definition of planet set 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.
The official definition of "planet" used by the International Astronomical Union (IAU) only covers the Solar System and thus does not apply to exoplanets. As of April 2011, the only definitional statement issued by the IAU that pertains to exoplanets is a working definition issued in 2001 and modified in 2003. That definition contains the following criteria:
Objects with true masses below the limiting mass for thermonuclear fusion of deuterium (currently calculated to be 13 Jupiter masses for objects of solar metallicity) that orbit stars or stellar remnants are "planets" (no matter how they formed). The minimum mass/size required for an extrasolar object to be considered a planet should be the same as that used in our solar system.
Substellar objects with true masses above the limiting mass for thermonuclear fusion of deuterium are "brown dwarfs", no matter how they formed or where they are located.
Free-floating objects in young star clusters with masses below the limiting mass for thermonuclear fusion of deuterium are not "planets", but are "sub-brown dwarfs" (or whatever name is most appropriate).
This article follows the above working definition. Therefore it only discusses planets that orbit stars or brown dwarfs. (There have also been several reported detections of planetary-mass objects that do not orbit any parent body. Some of these may have once belonged to a star's planetary system before being ejected from it; the term "rogue planet" is sometimes applied to such objects.)