Java on the web was very problematic in the early days, but implementations have gotten better and if you're out to make web accessible program with full desktop functionality, I'd say Java is a good choice. If you just want eye candy, Flash would probably be better IMHO.
But when it comes to playing multimedia on a web page, I prefer pages that let ME control the media that's playing, not some Flash or Java applet.
I only disable Javascript when I go to suspect sites. I know security concious people recommend disabling Javascript as default, but I think they're paranoid.
Javascript is supposed to be sandboxed so it can't hurt your computer, cross-site scripting is blocked, and as it's been around for years I would think most of the vulnerabilities have been fixed. Unless you're doing something shady like falling for phishing schemes or look for warez, is does enabled Javascript cause more problems than it fixes? I don't think so.
And we need something w/ Javascripts functionality, because there's a gap between what you can accomplish with declarative languages like SVG and SMIL, and what you need a full fledged programing language for (like Java).