80 Column Mind
Many browser based games use it, and some etailers use it in their checkout process (such as the process of adding things to your cart, or customizing), and if you do your banking and bill payments online you may not be able to do it without Java. But other than those, if those don't affect you, you may never use it.
Instead of deleting it I would suggest you do what I do and just use NoScript which, among other features, it blocks Java applets from launching. Since most all exploits require the person going to a malicious web page or run a malicious applet, it takes care of that problem, among others.
Oh for the day when Java and Flash are replaced by HTML5...
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