Update: See newer post for instructions on installing Firefox/Thunderbird 10 on CentOS and RHEL.
As of writing, the latest version of Firefox for CentOS is 3.6.22, and the Mozilla team released version 7 of the Firefox browser earlier this week. Obviously, the CentOS repository is slightly behind in keeping Firefox updated. However, if you wish to upgrade to Firefox 7, the process is quite simple. This tutorial has been tested on CentOS 5 and 6, under both 32 bit and 64 bit.
Update: This has also been tested successfully on 64bit RHEL 6.
The installation process varies slightly based on whether you are using 32 bit or 64 bit.
tar xf firefox-7.0.1.tar.bz2
Move Firefox to the proper directory
sudo mv firefox /usr/lib/firefox-7.0
sudo mv firefox /usr/lib64/firefox-7.0
Modify the Firefox command to use the new version of Firefox
sudo perl -pi -e 's/3.6/7.0/g' /usr/bin/firefox
Clean up unnecessary files
rm -rf firefox-7.0.1.tar.bz2