If you want to compile an exhaustive list of things that don't exist, you're welcome to try, but you're gonna be here a looooooong time.
"In the Universe as a whole, the conserved constants (electric charge, angular momentum, mass-energy) add up to/cancel out to exactly 0. There isn't any net electric charge or angular momentum. The world's positive mass-energy is exactly cancelled out by its negative gravitational potential energy. (Provocatively, cryptically, elliptically, "nothing" exists)"
'Dangerous' David Pearce
http://en.wikipedia.org/wiki/David_Pearce_(philosopher)
But I think the categorisation that groups believers, of any religion, into one set and atheists into another is much more important. In the same way that, while a Spurs fan and an Arsenal fan may consider themselves rivals (or even, in the case of some of the thicker ones perhaps, enemies), they nonetheless have much more in common with each other than either of them does with someone who couldn't give a shit about football.
Someone like Dawkins wants everyone to disavow the value of football.
I agree. It's a shame because some of his ideas are quite beautiful, mystical even, but he does come across as overly dogmatic these days.
I can see how he has issues with the ID posse, but for the most part science and 'religion' don't have to be mutually exclusive do they. In fact that kind of vociferous atheism could be seen as, if not a religion, then at least a category error. Some of what he would probably describe as 'non-scientific' ways of conceptualising and interacting with the world can be effective and rewarding, is it really so 'rational' to insist on ignoring that whole area of human experience?
The rules of football can not be 'proved or falsified' by science, it doesn't really make sense to speak of them in those terms, they are a creative construction, but they work to shape reality and experience and serve many functions for many people. And those same people are also free to play table-tennis, study chemistry and write bad poetry.