I'd say that a planet is a typically spherical world orbiting a star with a gravity that allows one to walk around on it and that is not considered a moon.Yes, I agree, with the slight change (as seen in David Levy's suggestion) that the gravity was sufficient to turn it into a spheroid. :') That brings in Ceres, Pluto, Eris, and some other outer Solar System objects. I've been trying to avoid using the term Kuiper Belt Object (KBO) because I don't think it's relevant any longer.
I like Levy's gravity-turns-it-into-a-sphere definition.
They should go with that and then just sub-quantify like they do with stars. Ok, we know what a star is, but there are red ones, yellow ones, little ones, big ones, etc.
With planets we have "terrestrial" (or silicate) planets, gas giants, and icy dwarfs. Why do the icy dwarfs have to be out of the picture? Pluto has the land area of Africa and probably Europe combined. It's a planet.