I've been using Ubuntu. It has been pretty stable. I am not really hammering it with anything. I basically have a mailserver running with squirrelmail as the retrieval tool.You can get it at http://www.ubuntu.com/
ubuntu is fine. Looked good the few times I've used it. Fedora is the most popular distribution that I've seen but I'm not sure if that's free anymore. Years ago (under the red hat name) it used to be free.
Fedora is free. Redhat is the commercial version that they sell and Fedora is the free version. http://fedora.redhat.com/
all versions of Linux are technically freeware. At every site that offers a commercial distro, there is a way to download the core OS...you have to pay for the extra goodies they throw in + tech support(and the packaging of course). normally these could all be found at http://www.linuxiso.org but they are down right now due to hardware failure. You can still find the isos...but you have to go to individual distro sites for now till linuxiso comes back online.
I like how the one distro mentioned in the OP (Red Hat) is the only Linux distro (that I know of) that's NOT freeware... Edit: And to add something useful... http://distrowatch.com/
Mandriva or Ubuntu. Both terrific distros -- I use Ubuntu on my other laptop. Ubuntu is what all the cool kidz are using these days, but if you want a professional-looking, polished distribution with lots of easy to use administrative tools, you can't beat Mandriva. http://www.mandriva.com/en/download/free -- scroll to the bottom for download mirrors. http://www.ubuntu.com/products/GetUbuntu/download#currentrelease
in our office we work with Ubuntu CentOS Fedora Core Scientific Linux Debian Pretty much the main ones, they all good. Just gotta find what you like.