There are very few cases to ever have Java actively installed in your browser. It still has desktop and app useage, but that's different than applets. You can't run Photoshop CS6 under El Capitan without the Java SE 6 runtime installed for instance.
If you have Java active in your browser here's what I suggest:
You can listen to vid1900 (I would) or you can listen to Alex (in this case, I would not), you can listen to me. Either way, do yourself a favor, and just go into your settings, and uncheck it. Turn it off. Restart your browser to be safe. Then try it. You know what will happen? Nothing. You won't notice a difference. And you'll be safer.
But here's my argument if you're interested:
We cover this stuff at Ars Technica (where I work) on a regular basis. We're a world renown publication when it comes to our security coverage. Don't listen to the creative director, look at the people who make it their job to understand these things. Look what our security editor, Dan Goodin, wrote just this last July for instance:
"Internet users should take renewed caution when using both Adobe Flash and Oracle's Java software framework; over the weekend, three previously unknown critical vulnerabilities that could be used to surreptitiously install malware on end-user computers were revealed in Flash and Java."
"Ars is once again advising readers to limit, or if possible completely curtail, use of both Flash and Java, at least until fixes for these three critical bugs are available."
— Source: http://arstechnica.com/security/2015/07/two-new-flash-exploits-surface-from-hacking-team-combine-with-java-0-day/
Once again. Because we say it all the time. Such as ...
"Ars has long advised people to assess if they truly required Java and other browser plugins and if not to consider uninstalling them."
— Source: http://arstechnica.com/security/2015/08/fake-eff-site-serving-espionage-malware-was-likely-active-for-3-weeks/
One of our other writers who covers the programming and security beats:
"Chrome 42, released to the stable channel today, will take a big step toward pushing old browser plugins, including Java and Silverlight, off the Web. Those plugins use a 1990s-era API called NPAPI ("Netscape Plugin API") to extend the browser, and with Chrome 42, that API is now off by default."
— Source: http://arstechnica.com/information-technology/2015/04/chrome-starts-pushing-java-off-the-web-by-disabling-plugins/
Chrome turned that shit off, and it's not coming back now. Chrome is a major browser heavyweight. And they don't even support it anymore. Does it really seem that necessary to you?