I don't have Java installed just for Minecraft, I code in Java for schooling. I honestly need it.
People you trust can redirect you to these websites, and that's actually how most of them spread.
It's not I who have fallen under general Java exploits; I am far too intelligent to become deluded from a simple Java exploit. I have seen many people get tricked by them, and most of the people who get infected think they're too smart for an anti-virus or anti-malware program. Enabling a whitelist for plugins on websites (NoScript is a perfect example of so, Opera has it integrated) boosts your security to the max. You honestly will never get a virus should you enable plugins on demand instead of leaving them enabled.