Funny thing is, there is no real consensus as to what exactly a species is. The most widely used definition is the biological species concept: if two organisms can breed and produce viable offspring, then they are the same species. But even this definition is very flawed.

There are cases where two species can produce viable hybrids. For example, grizzly bears (Ursus arctos horriblis) and polar bears (Ursus maritimus) have been known to occasionally interbreed in the wild, and their offspring are called grolar bears.

And of course, this definition doesn't even take into account the countless critters that reproduce asexually. Bacteria for a example reproduce through binary fission, in which the cells splits into exact copies of itself. They maintain genetic diversity through horizontal gene transfer, in which they just randomly exhange genetic material with one another.

Even if you count horizontal gene transfer as "mating" (which it really isn't, because this is not how they reproduce), bacteria can not only do this between different species, but even different genera. So the biological species concept pretty much goes out the window here.

In reality, the whole concept of a "species" is entirely arbitrary. It's just something that helps our little monkey brains understand the relationships between organisms.