"Web sites use Java to display graphics and moving images."
That'll be java script, not java as such (not the one that's prompting for the update anyhow)
Personally.... I'd uninstall java totally, see if it stops anything working, if everything you use still works you've got rid of one of the main security exploit targets on your computer.
If you remove java and it does stop something important working then simply install it again (link below) and make sure you do keep it up to date.
http://java.com/en/download/index.jsp