There used to be rumours that the Asteroid Belt was the remains of a planet that broke up, but I seem to recall several holes in the theory. It was spread over too large an area, the orbits made no sense and the mass of all the asteroids would need a rocky planet about twice the size of Earth, which went against physics, since the further out you get in the Solar System, the more likely you are to encounter light substances such as Hydrogen or Helium, not stuff like Silicon and Iron. What a lot of people don't realise is just how big the gap between Mars and Jupiter actually is, it's about the distance from the Sun to Mars iirc.
I suppose many things classify a planet, regular orbits/rotation times, minimal variance to axial tilt for a given value of 'minimal'. Abilty to gravitically hold lighter molecules, thus forming an atmosphere, evidence of multi-stage surface building etc etc, the list goes on....
