The applet I’m working on is rather specialised, so talking about that isn’t going to prove much. Others have pointed out some common examples from among the fields I mentioned, such as Minecraft, WebEx, and Danish government web sites. Each of these has a significant user base relying on Java applets.

Does Minecraft use applets or is it just a standalone desktop Java app? Does installing Minecraft create any vulnerability to this bug on a machine whose browsers have deactivated any Java plugin?

There are unrelated.

Besides downloading the Java app, you can play Minecraft in the browser through an applet at https://minecraft.net/play.

So no, if you are not running Java in the browser, a malicious web page can't run neither Minecraft nor other Java apps that you have locally installed.

Just about every out-of-band management card (e.g. HP iLO, Dell iDRAC) for server-class computers, uses the Java plug-in to present a KVM (keyboard/video/mouse) console through a web browser.

You don't mention where you work, but I'm guessing it's not an "enterprisey" or "corporatey" kind of place. Count your blessings :)

Things like this are pretty useful: http://hb9leb.no-ip.info/dspic/html/KaiserFilterDesign.html

Currently using it daily for Citrix/Juniper "Java Secure Application Manager" for remote XenDesktop access into a customer.

Online tax payments in Hong Kong uses a java applet.

Documentum from EMC uses Java as part of it's browser interface (webtop). It's used to download and manage documents on the user's machine.

You don't know anyone who plays Minecraft?