I may get slammed for this. I hope I explain clearly.
'Species' is a model, it is taxonomists who, quite sensibly, try to find some order in the biomass. Nature didn't invent species, man did. People typically picture 'a species' as a truly discreet unit, I know simple definitions such as the ability to interbreed are often used as explained above; this is fine for generalising. Life and nature is more fuzzy than we would like the 'ring species' are a good example
http://en.wikipedia.org/wiki/Ring_species
I think, I may be wrong, but in the same fashion as the species changes along a distance transect for the ring species, a temporal transect would show a similar pattern. By this I mean a sequence of organisms with very little difference between them spread out over time. When people talk of 'missing links; in fossil records or similar I think the confusion is based around the same misunderstanding.
We talk of visible light, IR, X-ray - these are 'species' in a sense. The EM spectrum is exactly that, a continuum. Scientist have spit it up into more convenient units, the cut off points between different types of EM radiation may be in places for good reason, but they aren't truly discreet since there is continuity between them.
DNA analysis is making taxonomists move the odd organism across entire groups, convergent evolution makes it difficult to assess a species on looks and habits alone. It also seems that there can be bigger (%)genetic differences within a population of a certain species than between some species.
I also see the concept of 'race' in a similar fashion. I don't really follow it so well as once again the lines between who is and isn't in a certain group aren't exactly scientific. Maybe we could make assessments based on Neanderthal/Denisovian DNA or lack of in a human? Least it would be less subjective.