Yes, it is good to keep Java updated. On the other hand, it is best to disable it in your browser unless it is needed for something meaningful. Java is not necessary for general surfing, and it can be used maliciously. I always disable it unless I am running my browser sandboxed (in a virtual environment that keeps all downloaded files separated from the operating system).
Javascript -- which, despite the name, has nothing to do with Java -- can also be used for evil purposes, but it is used by so many sites, especially forums like this, that it must be enabled. Unlike Java, there is no javascript update per se, but keeping your browser updated will help to prevent damage from mis-used javascript.