According to J. Richard Gott the Third
Humanity has between 5,100 and 7.8 million years left to exist, with
the actual number somewhere in the middle.
More here:
http://en.wikipedia.org/wiki/J._Richard_Gott
I assume this assumes he is referring to humanity as the species
currently exists. We could continue to survive in an altered state,
either biologically or artificially. We certainly have the potential to
outdo natural selection and should not wait around for Mother Nature,
as she could certainly knock us out long before then. Just ask the
dinosaurs or trilobites.
Oh wait, you can't.