A world in which Java (the run-time) suddenly disappeared would be completely non-functional due to the amount of enterprise software that runs on the JRE. And while Java (the language) is often bashed for it's verbosity, many of the up-and-coming, "cool" languages target the JRE as their run-time environment.
Unfortunately, burying that paragraph in a long article and stating "you probably don't need it" is the wrong story to tell. You probably couldn't live (your modern life) without it, but you may not need to have it installed on your computer.
EDIT 1:
I also should have mentioned that Javascript is not "safe" ... it's "safer" than it used to be because browsers have gotten way better at "sand-boxing" its behavior (I love LocalStorage!). Applets were designed to allow browser-based applications access to the underlying computer's OS, so it should be no surprise that there are more vulnerabilities. And if you think about the biggest attack vectors on the IE browsers (at least the older ones), ActiveX shares this trait (I won't call it a problem).
For Android users, you should realize that when you authorize applications to use various features of your phone or tablet, you're explicitly opening holes in Android's default security model (fully sand-boxed).
EDIT 2:
My favorite quote (so far) on the life-hacker site is "Java does have some legitimate uses (namely Minecraft) ...". The rest of his commentary sounds like the rants typically found in language wars (I won't participate).