As a layman my go-to definition of a species used to be the one given by Bamberg below (and for all practical purposes it still makes sense). Modern human races can interbreed and have fertile offspring. Therefore they don't constitute different species.

It turns out the concept of species is dated or at least doesn't fit all the phenomena out there: http://biology.stackexchange.com/questions/39664/how-could-h...

So, I suppose one could argue to some extent that Neanderthals were a human race rather than a species of their own.