OpenJDK (Open Java Development Kit) is a free and open source implementation of the Java programming language. OpenJDK however isn't bundled with the web browser plugin which is a part of Oracle Java.
Fortunately the IcedTea-Web project provides a Java web browser plugin.
On RHEL6 and its clones, icedtea-web depends on java-1.6.0-openjdk and will pull it as a dependency.
In practice, on CentOS 6.2 and Scientific Linux 6.2 if you want to have Firefox working with a Java plugin simply install icedtea-web, like so:
# yum install icedtea-web
Launch Mozilla Firefox and in the address bar enter about:plugins.
Also you can point Firefox to http://www.javatester.org/version.html and check if you have the Java Run-Time Environment working.
Now we can all submit our tax reports ;)