Is there a free (as in money) version of Redhat linux?
CentOS is essentially RedHat Enterprise with the stuff they can't include (i.e. RedHat specific stuff that isn't licensed for free redistribution) removed.
CentOS tends to be closer to RH Enterprise as it is based fairly directly on it, where Fedora tends to be a bit more leading-edge.
Update (2019-Nov) as this is still getting views and the occasional upvote: since this answer was written the market and the status of CentOS within it has changed a bit. RedHat and the people behind CentOS have worked more closely, in fact since 2014 RedHat has actually been providing funding for the project. See https://en.wikipedia.org/wiki/CentOS#History, amongst many other references.
If you are looking for Red Hat Enterprise Linux . thats not free.
Fedora is a Linux-based operating system that showcases the latest in free and open source software. Fedora is always free for anyone to use, modify, and distribute. (http://fedoraproject.org/)
The Fedora Project is a Red Hat sponsored and community supported open source project. Its goal is the rapid progress of free and open source software and content.
Several people have pointed out the CentOS is a Free drop-in replacement for RedHat Enterprise Linux.
Just a note about the history and where it stands now: RedHat (The company) used to release RedHat Linux for free and also charged money for it. They eventually added new variations of RedHat Linux including server editions, etc. The free product was discontinued and they were focussing on their Enterprise products, for which no binary download was available. However, they have to release the source, so the CentOS folks stepped up and release a free, re-branded RHEL with any proprietary bits removed.
For the "desktop"/"community" users, RedHat started the Fedora project, which serves as a free desktop Linux (the technology can be used for servers) and a testing ground for future RHEL releases. Fedora isn't as suitable for production use because it's not supported for very long so you have to upgrade the whole distribution frequently. But it is free.
So, to sum up, Fedora and CentOS are both free, neither is RHEL, but CentOS is close.