Though the universe contains billions upon billions of stars, until recently only nine planets were known -- those of our solar system. The Solar System provides a fundamental model for what we might expect to find around other stars, but it's difficult to form generalities from just one example. It may turn out that nature is more varied and imaginative when it comes to building and distributing planets throughout the Galaxy.
In it simplest definition, a planet is a nonluminous body that orbits a star, and is typically a small fraction of the parent star's mass. Planets form out of a disk of dust and gas that encircles a newborn star. These embryonic disks have been observed around young stars, both in infrared and visible light. The planets' orbits in our solar system trace out the skeleton of just such a disk that encircled the newborn Sun.
Planets agglomerate from the collision of dust particles in the disk, and then snowball in size to solid bodies that continue gobbling up debris like cosmic Pac-Men. In the case of our solar system this led to eight major bodies, thousands to tens of thousands of miles across. (The ninth planet, Pluto, is probably a survivor of an early subclass of solar system inhabitants called icy dwarfs). A planet's mass and composition are determined by where it formed in the disk. In the case of our solar system the more massive planets are found far from the Sun, though not too far where material didn't have time to agglomerate (because orbital periods were so slow that chances for collisions were minimal).
Unlike asteroids which are cold chunks of solar system debris, a planet must be massive enough to have at least once had a molten core that differentiated the planet's interior. This is a process where heavier elements sank to the center and lighter elements float to the surface. According to this idea, planets should have dense rocky/metallic cores. Depending how far they formed from their parent star, they may retain a dense mantle of primordial hydrogen and helium. In the case of our solar system this establishes two families of planets: the inner rocky or terrestrial planets such as Earth and Mars, which have solid surfaces, and the outer gas giant planets Jupiter and Saturn that are mostly gaseous and liquid. Massive planet like Jupiter are still gravitationally contracting and shine in infrared light.
Ironically, the first bonafide planetary system ever detected beyond our Sun exists around a neutron star - a collapsed stellar core left over from the star's self-detonation as a supernova. Resembling our inner solar system in terms of size and distribution, these three planets orbiting the crushed star probably formed after the star exploded. Apparently a disk must have formed after the stellar death, from which the planets agglomerated. Other suspected extrasolar planets also seem to defy conventional wisdom. An object orbiting the star 51 Pegasus may have the mass of Jupiter, but is 20 times closer to the star than Earth is from the Sun.
