Now that the IAU has officially declared the fifth dwarf planet (in order of size: Eris, Pluto, Makemake, Haumea, Ceres), we are likely in for a dry spell on new dwarf planets. The preliminary searches of the sky are all but complete, and (as far as I know) no one has any new objects the size of Haumea hiding in their back pockets. We'll probably be at five official dwarf planets for a while.
Now is a good time, then, to remind ourselves what a dwarf planet really is.
When the final vote on the definition of "planet" was made, and the eight dominant bodies in the solar system were declared (quite rationally) a class separate from the others, a new class of objects was defined. The "dwarf planets" are all of those objects which are not one of the eight dominant bodies (Mercury through Neptune) yet still, at least in one way, resemble a planet. The best description I can come up with is that a dwarf planet is something that looks like a planet, but is not a planet. The official definition is that dwarf planets are bodies in the solar system which are large enough to become round due to their own gravitational attraction.
Why do astronomers care about round? If you place a boulder in space it will just stay whatever irregular shape it is. If you add more boulders to it you can still have an irregular pile. But if you add enough boulders to the pile they will eventually pull themselves into a round shape. This transition from irregularly shaped to round objects is important in the solar system, and, in some ways, marks the transition from an object which is geologically dead and one which might have interesting processes worthy of study.
[Haumea is, of course, not round, but that is only because it is spinning so fast. If you stopped it spinning it would become a sphere. That still counts.]
So how many dwarf planets are there? Five, of course. The IAU says so.
But let's ask the more scientifically interesting question: how many (non-planet) objects in the solar system are large enough to be round due to their own gravitational pull?
Still five, right?
Well, no. Here is where the IAU and reality part ways.
There are many more objects that precisely fit the definition of dwarf planet but that the IAU chosen not to recognize. But if the category of dwarf planet is important, then it is the reality that is important, not the official list. So let's examine reality.
So how many dwarf planets are there? Ceres is still the only asteroid that is known to be round. After that it gets complicated. All of the rest of the new dwarf planets are in the distant region of the Kuiper belt, where we can't actually see them well enough to know for sure if they are round or not.
While we can't see most of the objects in the Kuiper belt well enough to determine whether they are round or not, we can estimate how big an object has to be before it becomes round and therefore how many objects in the Kuiper belt are likely round. In the asteroid belt Ceres, with a diameter of 900 km, is the only object large enough to be round, so somewhere around 900 km is a good cutoff for rocky bodies like asteroids. Kuiper belt objects have a lot of ice in their interiors, though. Ice is not as hard as rock, so it less easily withstands the force of gravity, and it takes less force to make an ice ball round.
The best estimate for how big an icy body needs to be to become round comes from looking at icy satellites of the giant planets. The smallest body that is generally round is Saturn's satellite Mimas, which has a diameter of about 400 km. Several satellites which have diameters around 200 km are not round. So somewhere between 200 and 400 km an icy body becomes round. Objects with more ice will become round at smaller sizes while those with less rock might be bigger. We will take 400 km as a reasonable lower limit and assume that anything larger than 400 km in the Kuiper belt is round, and thus a dwarf planet. We might be a bit off in one direction or another, but 400 km seems like a good estimate.
How many objects larger than 400 km are there in the Kuiper belt? We can't answer this question precisely, because we don't know the sizes of more than a handful of Kuiper belt objects, but, again, we can make a reasonable guess. If we assume that the typical small Kuiper belt object reflects 10% of the sunlight that hits its surface we know how bright a 400 km object would be in the Kuiper belt. As of now, about 50 objects this size or larger are known in the Kuiper belt (including, of course, Eris, Pluto, Makemake, and Haumea). Our best estimate is that a complete survey of the Kuiper belt would double this number, so there are roughly 100 dwarf planets in the Kuiper belt, of which 50 are currently known.
The new dwarf planets in the solar system are very different from the previous 8 planets. Most are so small that they are smaller across than the distance from Los Angeles to San Francisco. They are so small that about 30,000 of them could fit inside the earth.
Does it matter how many dwarf planets we say there are?
I think the answer is "yes." If you believe that there are only 4 dwarf planets in the Kuiper belt then you place an oversized importance on those 4 objects and you get an exceedingly warped picture of what the outer solar is like. The important thing about the Kuiper belt is that beyond Neptune there are many many many objects with hundreds being large enough to be round. The four "IAU Dwarf Planets" in the outer solar system are all fascinating objects -- hey! I discovered 3 of them, I must think there are at least a little interest -- but it would be a gross exaggeration to think of them as the only objects, or even the only important objects, in the fascinating region of space beyond Neptune.