I find it interesting how there has been so much news buzz lately over whether we should consider Pluto a planet or not, given that there are other objects of similar or greater size. For one thing, I wonder about this obsession with size; why would one make the line between planets and non-planets size-dependent, as if it weren't possible for objects orbiting the sun to come in enough sizes that the line would certainly be arbitrary? It's like using a size-criterion for satellites. This would obviously be absurd, since satellites come in all sorts of sizes; what matters for a satellite is that it be orbiting a more massive body.
Since a great deal of it is arbitrary, anyway, here's my two cents. The first and most fundamental criterion for determining what counts as a planet is that a planet must be a 'wandering star', which basically means:
(1) It must be close enough that its path can be traced across the heavens relative to the stars, taken as fixed for our purposes.
(2) It must be visible from earth with equipment detecting visible light reflected from the sun.
(3) It must be orbiting the sun in a regular way.
(4) It must be fairly stable in mass and shape (e.g., not disintegrating).
None of this rules out much, of course; but I propose that everything that meets (1)-(4) be called a 'planetary object'. This would include all sorts of things, like moons. We usually think of the planets as being spherical bodies dominating a sphere of the heavens -- we may not put it in explicit Ptolemaic terms quite like that, but we do think of them in this wise. So:
(5) It must be approximately spherical ('its self-gravity must be enough to overcome rigid body forces' as some people like to say).
(6) It must be the gravitationally dominant object in its immediate region of orbit.
Things that don't fit (5) can be called 'asteroidal planetoids'; things that fit (5) but not (6) can be called 'satellite planetoids'. (Note that it isn't important as to 'how spherical' it is; some things don't approximate a sphere at all, and others do. The ones that clearly do clearly fit the criteria.) There might need, however, to be a special intermediate category of 'geminal planets' or 'geminal planetoids' for possible (1)-(5) objects that are revolving around each other in their path around the sun, but that have very close to the same mass (so neither dominates, although together they are significant). Planetary objects fitting (5) and (6) can be called 'planets'; and it does not matter what size they are, how distant they are, or anything else, as long they fit the criteria. (6) is, I think, very important; one of the most common distinctions we make with regard to planets is to distinguish them from satellites of planets, and this is much more important for deciding what's a planet than size is.
So 'planet' should be the label for a stable, roughly spherical, sun-orbiting object, visible from earth by visible light, that is not a satellite to another sun-orbiting object; or, at least, the conditions for the label should be something along these lines. We can then use the size classification often suggested, namely, dividing planets into giant planets, terrestrial planets, and dwarf planets. Even if my criteria need to be tweaked here and there, they provide a reasonable stable means of classification that doesn't do much harm to common classification (although it diverges a bit from some suggested classifications that haven't become common) but which gives some reason for us to talk about planets without being purely arbitrary. Of course, it has disadvantages, too; but so does every set of conditions.