Is Pluto a real planet, or just a large asteroid? What is the definition of a planet, anyway?
The question of whether Pluto is or is not a planet is very popular among the public. However, most professional astronomers do not think this is a question of that much importance, as the dividing line between a planet and an asteroid is somewhat arbitrary. Still, there are good arguments for supporting either view:
1) Historical. Pluto was discovered long before other Kuiper Belt Objects (large asteroids that orbit in the same region) and at that time "planet" was the only available label for something like Pluto. So people argue that since there is nothing to gain from demoting Pluto, we should just leave the things as they are.
A weakness in this argument is that demotions are sometimes necessary if an important observational result is proven wrong (i.e. object is actually much smaller than we though). From its discovery in 1930, and up until 1978 when Pluto's moon Charon was discovered, Pluto was though to be larger than Mercury and possibly even Mars (in reality, it's much smaller in mass than either of them). Would the astronomers designate Pluto a planet in 1930 if they knew how small it really was? I think that the answer is still yes, but there is no real way to confirm that.
2) Size. Pluto's mass is 25 times smaller than Mercury's and only 9 times larger than that of Ceres, the largest body in the asteroid belt. Some recent large Kuiper Belt Objects (notably Sedna) are likely larger than Ceres, if smaller than Pluto (and the recently discovered Eris (previously "Xena" or 2003 UB313) may be larger than Pluto). However, any lower cutoff in size for planets is arbitrary, and putting it above or below Pluto's size and mass is a question of individual preference. Also, if, for example, the lowest diameter a planet can have is 2000 km, then a body with diameter of 2001 km in a planet while a body with 1999 km diameter is an asteroid. To make things worse, planetary diameters are rarely known that accurately before direct exploration by spacecraft, which is not always an option.
3) Environment. Our solar system can be roughly divided into two kinds of regions: those where major planets orbit, which are mostly free of small bodies, and the regions where there are no planets and where many small bodies orbit (the examples of the latter are the asteroid belt and the Kuiper belt). While this division is not perfect (comets and some asteroids do cross planetary orbits, but these are few and their orbits are unstable), it does reflect an importanty fact that a planet's gravity strongly influnces its surroundings, while asteroids affect each other mainly by direct collisions.
Mike Brown of Caltech and his colleagues have recently proposed that population of small bodies which may share the orbit with the candidate body should be taken into account when defining a planet. They propose that if a body's mass is greater than the total mass of small stuff which orbits in the same region, it is a planet. So, Mercury might not be too big, but since very few asteroids orbit the Sun in its vicinity, it is definitely a planet. Jupiter shares its orbit with numerous so-called Trojan asteroids, but their total mass is negligible compared with that of Jupiter, so Jupiter is also a planet. Pluto, according to this criterion, is not a planet, because its mass is smaller than the estimated total mass of all other Kuiper Belt Objects.
The theory behind this definition is that once an object is large enough it would "sweep up" smaller bodies in its vicinity, leaving its orbit empty except for itself, few transient interlopers (comets etc.) and maybe a resonant population with a small mass (e.g. Trojans). Eight major planets managed to do this, but not Pluto, which is not a major influence on the Kuiper Belt.
While this definition of a planet is probably the most objective one proposed so far, there might be practical problems with it. It is unrealistic to expect that a classification of a body has to be delayed until the neighboring region has been thoroughly explored. This might not be possible for decades in the case of most extrasolar planets, or even some very distant bodies in our solar system (like Sedna, for example).
The bottom line is that if Pluto were discovered now, most likely we would not call it a planet. However, most astronomers think that a change in Pluto's status would be of limited usefulness while confusing, so it will probably continue to be considered a planet. The exact and universal criteria on what constitutes a planet are not agreed upon yet, and we might need to wait for many years until most scientists agree on one.
Update Aug 2006 by Karen Masters: The International Astronomical Union (IAU) voted this month to redefine a planet much a long the lines that Matija discusses above. There is both a size limit, and a requirement that the object sweep out its orbit. In addition the object must independently orbit the Sun (excluding several large moons of Jupiter). This new classification redefines Pluto as a "dwarf planet", leaving the Solar System with 8 "classical planets". New additions to the dwarf planet class are Sedna, the largest asteroid, Ceres and Eris (previously "Xena" or 2003 UB313). Many more objects may join the class, pending more accurate determinations of their size, including Quaoar, and several other Kuiper belt objects. This definition followed an earlier suggestion that all objects independently orbiting the Sun which have sufficient gravity to become roughly circular should be called planets - such a definition could have dramatically increased the number of planets. Dynamical astronomers (like Matija) argued that the orbital criteria (that the object dominate its orbit) was equally important, thus excluding Pluto, and these many other small objects from the "classical" planets.
This new definition of planets which exludes Pluto has caused a lot of interest and discussion, with Astronomers and the general public alike coming out loudly on both sides of the argument. I think it's safe to say that any decision by the IAU would have upset someone, but putting the definition of a planet on an objective scientific footing will likely (ultimately) be popular with Astronomers. Pluto will always retain a special place in our hearts, having been considered a planet for over 3/4 of a century and with a NASA mission (New Horizons) on its way to reach the Pluto-Charon system in July 2015, Pluto will not be forgotten.
This whole episode also gives an interesting insight into the scientific process of object classification and the changes which must be made to schemes in the light of new scientific information.