Well (http://en.wikipedia.org/wiki/State_of_matter) has got tricky the refer to the 3 chemistry states gas,liquid, solid as classical states.

If I counted correct they list 17 non classical and I can think of a couple of weird ones they didn't list like suprconductivity states.

But some of these get weird because they are only human made QM ones like when they hollow out the electron shells using hard x-rays (http://www.physorg.com/news197123979.html).

So I am guessing 20-30 by end of it all .. bags not teaching it to students, 3 was so much easier :-)

When we get time someone is going to have to work out how to put a nice story together everyone is to busy doing at the moment.

I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.