Never installed the Java Run Time Environment and haven't come across a site which requires Java. Please give me some "standard" sites which need it.

This is a very difficult question as some sites with java that I go to may not be of interest to you. I know that my ISP in Oman uses java.

This is the problem with this new browsers. You never know when you need java until
you come across a site that needs one. So there goes your "small foot print browser" which in the long run needs 8mb for the java.

Yahoo games, for example, use Java

In addition to game sites also science sites also use Java for simulations & demonstrations, some commercial sites for realtime stock (or whatever) info. Usually specialized sites with very specific implementations.

My online banking site requires Java in order to operate, and to be quite honest I'd much rather have them use Java than an Active X control.

this is a fairly concise example of a site that uses java, but also works without it:

http://www.time.gov/

In my browsing experience - unfortunately - most sites that use java are not using it for anything useful, but only to do fancy show-off stuff. Some things that some people may consider "useful" are weather reports (jeez crumbs, I have a radio for that), stock market reports (nice if you have money)...
If you get into artsy and fractal-oriented sites you may encounter some heavy java barrages (of the fancy show-off type), often on the entry page. I have run across more than one Wow Look At This Wonderful Java Demo Of My Awesome Screensaver affair, none of them what I would call Art for the Ages...LOL Game sites tend to have a lot too, I guess; I don't do them much.
Yes, I often wonder why I installed it, but there are some useful programs. I leave it in my browser prefs because I have a masochistic optimistic side. Some day I hope to find something worth it all... There have been a few good moments - sorry I can't remember where!
You are probably better off without it unless you should happen to need it for some essential business purpose, godforbid. It slows everything down horribly. Then there is the wonderful feeling you get when you have ten windows open, haven't even looked at half of them yet, nothing saved, and the next window you open gags on a ton of java and you have to three-finger the whole show. :p
I give a java-heavy site one minute to get its s--t together, and back out or kill the window if it takes longer. I want information, not masturbation - that's why I use K-M. ;-) I don't feel that I am really missing anything by staying away from those sites. Empty calories.

I dislike Netscape's default settings. The average person doesn't know much about the settings and have Java and JavaScript turned on all the time and then complain their net connection, PC, browser is really slow...

Polo, you keep constanty placing Javascript & Java into same sentence

They are two *very* different things. They have no connection of whatsoever. Regular Javascript doesn't make you PC slow. Javascript has been around and actively used since Netscape 2 and remember, what kind of hardware we had back then?

Yeah I know they are different things. But I tend to have JS off unless it is needed. I find a slight speed improvement without it...

I just remembered one java thing that is really rather good - Web Brain
http://www.webbrain.com/html/default_win.html
I think it's the main (only?) reason I keep the java on.
I don't drink a lot of coffee either ;-)
I always have javaScript on, it seems more universally used/useful... heck, I use it myself.