With the almost weekly Java exploits it is a best security practice to disable Java in your browser. FireFox on Linux will do this automatically. (See about:plugins to check this)
Some applications like WebEx still rely on Java on Linux. here are the ways to get the Oracle Java Plugin integration working after downloading the very latest Oracle Java JRE if you need to have it running:
#install latest RPM from Oracle
rpm –i jre-7u17-linux-x64.rpm
#Configure it as the default Java install
alternatives --install /usr/bin/java java /usr/java/latest/bin/java 20000
alternatives --install /usr/bin/javaws javaws /usr/java/latest/bin/javaws 20000
#Configure the Java plugin for 64-bit Firefox
alternatives --install /usr/lib64/mozilla/plugins/libjavaplugin.so libjavaplugin.so.x86_64 /usr/java/jre1.7.0_17/lib/amd64/libnpjp2.so 21000
#Check it is indeed being used
alternatives --display libjavaplugin.so.x86_64
#Test. Be sure that the version displayed is the version installed
firefox http://www.java.com/en/download/testjava.jsp