Just doing some back-of-the-envelope calculations…
The Wiki article on the most recent human ancestor gives the number as 2,000-4,000 years ago.
I used an average lifespan of 35 years (arbitrary, but I figure high mortality at that point would skew the average to the low end.)
So that gives you between 57 and 114 generations to that point.
Going back further, from Wiki (quoting Richard Dawkins):
Another way of looking at this is to say that our (approximately) 250,000-greats-grandparent was a creature from which all humans, chimpanzees and bonobos are directly descended. Further on in Dawkins’ imaginary journey (imaginary, in that the journey is going backwards in time), we meet the concestor we share with the gorilla, our next nearest relative, then the orangutan, and so on, until we finally meet the concestor of all living organisms, known as the last universal ancestor.