Most people are familiar with what is called the Biological Species Concept, which defines species as a reproductively isolated group of organisms that can all interbreed among themselves and produce fertile offspring. This works pretty well for most animals, but terribly for plants and many animals. Plants that are quite different can interbreed frequently, but do not because they are isolated by things such as flowering time, pollinator species etc... Then you get into weird intransitivity issues such as: population A can breed with population B, population B can breed with population C, but A and C can't breed.
These issues mean that a species is not a very well defined thing anymore. There have been many attempts to unify what we understand about the biology of reproductive isolation and genetic differentiation into one species concept, but we are left with many different "species concepts". I can't remember them all, but many are based genetic differentiation. It becomes crazy because under some gene-based concepts you could be defined as a species for one gene analysis and not another.
There is a new idea which may have showed up on slashdot that is called the genetic bar code and those scientists believe that there is one (or just a few) genes where a specific amount of differentiation in this area will define a species. They predict that they can create a machine that you can just put tissue samples in and have a determination of what species it is within minutes. It is a controversial line of research, needless to say.