First of all, we can't apply that definition of species dogmatically to Neanderthals and humans because we are unable to tell by looking at their bones whether they were capable of interbreeding. Originally they were considered to be a subspecies, so one would think that they almost certainly would have been capable of interbreeding, but currently it is thought that they represent a distinct species. So it is unknown whether or not interbreeding would be genetically possible.
Secondly, even assuming that interbreeding could produce viable offspring, there are many other variables that can reduce the odds of interbreeding to zero. There are many species that are capable of interbreeding artificially but do not in nature because of behavioral and physiological constraints.
Probably the most significant factor to be considered in interbreeding is the intelligence of the species. We all know that modern humans are quite adept at dividing groups into Self and Other. For humans, Neanderthals would have been decidedly Other. We don't know if Neanderthals had this same tendency towards bigotry (most likely, since it has adaptive value), but we do know that they were fairly insular, living in small family groups, not travelling very far, and not engaging in trade to any great extent. This makes alliances between the species unlikely.
Because the Neanderthals seem to have been fairly insular it is unlikely they would welcome a human male into their population. They may have felt differently about human females. However, they probably would find it difficult to get their hands on them considering humans considered women to be a valuable commodity. Because of this, they would be unlikely to allow the small bands of Neanderthals to steal women. On the other hand, humans would be unlikely to allow a Neanderthal male (Other and male to boot) into their group to mate with a human woman. They might be more accepting of Neanderthal women, but in general they probably considered human women preferable.
All of this would have been compounded if it is true (as some have argued) that Neanderthals had not developed sufficiently for complex language. It is certain that they could make a wide variety of vocalizations, but it's hard to say if they had speech.
All of that makes sense - but what basis is there for it?
Let's say for the sake of discussion that some alien invaders from Galaxy X were studying us and scratching their heads saying "Surely the humans and chimps interbreed. Look at how similar they are." I realize this is a far stretch, but imagine looking at humans and chimps for the first time and thinking they must be pretty closely related, and possibly even interbreed. Just like SampleMan (I think) made the analogy of the fox and the dog. And the offspring of horse and a donkey is unable to reproduce.
My personal theory is that there was no interbreeding, more along the lines of the horse/donkey scenario, otherwise as homo sapiens became more abundant on the Neanderthal turf, interbreeding would have become more prolific. This would have given the Neanderthals more human-like qualities thereby increasing their chance of survival, or would mean that eventually Neanderthal and homo sapien would merge into one species.
Certainly I'm not as well read on this subject as some of you brainiacs, but have always found it fascinating and wanted to chime in! :-)