How likely is it that Earth has millions of different species?
We can be reasonably certain that ALL species that exist today share a common ancestor, a common origin. Every single species we have even encountered, for example, uses a long chain of nucleotides (DNA or RNA1) to store its genetic information. If life had arisen through multiple independent sources, we would expect to find different solutions to the problem of passing genes to offspring. 

To put it another way, all forms of life we have found can be placed in one of three main classes (superkingdoms): eukaryotes, prokaryotes and archea. All other types of life come under one of those three categories (viruses are special and not really considered alive2):



Now, any organism we have ever seen uses the same basic systems of storing its genetic information. In fact, there are even certain genes that are conserved (similar in sequence) across all domains of life (see my answer here for some examples). That is why this version of the tree has a common root. All lines start from a single original line (commonly known as the Last Universal Common Ancestor, LUCA).

In summary, all the evidence we have points to a single origin of life. There are too many shared features to assume multiple origins. Despite their enormous diversity, all organisms share certain very basic systems. 



NOTES


As far as I know, only certain viruses use RNA instead of DNA, all truly living creatures use DNA. Even if I'm wrong about this, the differences between RNA and DNA at this level are small enough that the common origin still holds. 
See here for more in why viruses are not alive.