There are still some applications that need it, and if you are programming in Java then you need the JRE but in general, no. In general it is not needed on private computers. By default, Safari and other browsers will not run Java automatically, but at least ask you if you want to enable it for that site, when it’s installed. Safari’s controls over Java are quite separate, and part of the Websites section of its Preferences. It is insane to go around running every application you come across on the internet.
Java is just as safe as any other programming language. It’s safe to delete Java as long as you aren’t using it. You may ask, Should I remove Java from my Mac? But, again, even if you did install Java, the odds are very, very good that you aren’t running a vulnerable version. Many users do install Java for websites or applications (like Crashplan) that require it. The first, and most important, reason is that relatively few Macs are running the vulnerable version of Java.