It's a simple enough question, right? The answer is 9, surely? Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto.
Well that's what I thought, anyway, based on what I learnt at school back in the 1970s, and have read ever since in science books and the like. But apparently, back in 2006 (and I only just found out about it, so please forgive my ignorance if you already knew) it was decided by "the powers that be" that Pluto is no longer a proper planet, but is in fact a "dwarf planet", so there are now only 8 major planets in our solar system, not 9.
If this sounds crazy, confusing, or even perhaps makes you a bit angry to hear that Pluto is no longer officially considered to be a true planet, please bear with me for a few minutes and read on...
Pluto's reclassification was decided by the International Astronomical Union (IAU for short; the world "governing body" of all things astronomical) after very protracted deliberations during the IAU's 2006 General Assembly, and if you click on this Wikipedia "
dwarf planet" link, you can see what happened and why.
In short, quite a few new "heavenly bodies" were discovered outside the orbit of Neptune between 2000 and 2005 (called trans-Neptunian objects, most of which were found by teams led by a brilliant Caltech astronomy professor named Mike Brown), all of which are planetoid in form, and one of which - named Eris, discovered in 2005 - is actually larger than Pluto.
At the time of its very surprising discovery, Eris was nominally classified as our solar system's 10th planet due to it being bigger than Pluto. But this led to some heated debate within the global astronomical community, because really Eris is only similar to Pluto and is quite different to the other 8 major planets, and also because Pluto itself is only really similar to Eris and not the other 8 planets (Pluto has always been a bit of an "oddball", with its very small size compared to the other 8 planets, and its non-standard highly eccentric and highly inclined orbit), and this is what eventually led to Pluto's reclassification.
It is still a controversial topic in some quarters, in the public domain as well as between some astronomers and a few other scientific groups. Again, please read the relevant
Wikipedia article. It is all explained in great and excellent detail there, it all makes perfectly logical sense, and there is no point in my trying to reproduce it all in further detail here. Please read it, digest it and learn something new and really cool! :-)
So,
to answer my original headline question, and in summary, the new (almost) universally scientifically accepted definition of our solar system, as of September this year, is as follows:
There are 8 major planets orbiting our sun: the 4 rocky inner-planets Mercury, Venus, Earth and Mars, and the 4 gas giant outer-planets Jupiter, Saturn, Uranus and Neptune (which are separated from the inner planets by the asteroid belt);
and... wait for it...
There are also 5 dwarf planets orbiting our sun: surprising little
Ceres, which is in the asteroid belt between Mars and Jupiter, good old
Pluto, and the lovely new trio of
Haumea,
Makemake and
Eris.
Additionally, there are also a number of other trans-Neptunian objects (TNOs) that don't currently fit into the dwarf planet category (such as
Sedna, for example), plus a huge number of asteroids and comets, all also orbiting our sun.
It is fully expected that many more dwarf planets/TNOs will be discovered in time, as our technological ability to detect them improves, and so it is quite clear that we live in a far more dynamic solar system than the classic and rather static old "9 planets and 1 asteroid belt" model that was pretty much the standard until relatively recently. Currently the new definition looks a bit like this (click on the picture to see a larger version of it):

Personally, I love the new definition of our solar system. If you really think about it, Pluto is still considered to be a type of planet, just a new special type that is distinctly different to the major group that it formerly belonged to. I really like the fact that, if you (perhaps over-)simplify the new definition a little, there are currently 13 known "planets" in our solar system, with likely many more still to be discovered/classified in the future. Wow!