Is there a free version of Mac OS X?
The short answer is, as others already said, there is no free OS X.
The long answer is this: An operating system consists of many parts and large parts of OS X are indeed free. If you are interested in this have a look at the Darwin project.
What is missing from Darwin is mainly the graphical user interface of OS X (Aqua). You can run GNOME or KDE instead if you like. One of the consequences is that you can't run applications that depend on Aqua, like Safari or iTunes.
And just not to give false hopes: Darwin is very cool if you are interested in operating systems but in my opinion it's not very useful for most practical purposes.
You can't get Mac OS X for free, at least not legally.
OS X updates tend to be free - but IIRC its between consecutive versions, and you need to have apple hardware, or a running system. There's no way to 'simply' download an ISO and install it on an arbitrary system. Annoyingly for a reinstall there's no 'iso' download - you could in theory build an installer off of an ESD if you did have a mac and internet recovery is your best bet/supported bet for a bare metal install.
I'm assuming that's not what this is about. You'd want to run this on arbitrary hardware.
As of 2016. Nope. There's been a few attempts - you could get the kernels free for a while (there seem to be versions here), and attempts to throw together a functional userland around that - puredarwin at least has a webpage, but is not really there.
Kernels are lovely. Also entirely useless on their own. Get a usable userland and you can run the otherguy's stuff. For that matter, apple keeps its userland close to its chest, and that's the big pain point. Darling might help with that, you'd essentially need to port that back to darwin, which would be wierd. You can't simply download the GUI elements of OS X in any way.
In short, the fragments of a usable 'free' OS X 'compatible' system exists, but is in no way usable, and there's no official legal gratis release of OS X. There's pirated/hacked ones, but those are out of the scope of this site.