I'm afraid people do use it; of course the banks and so on (who probably can migrate to better solutions fairly easily); personally, I have a site that's pretty active this time of year, with music theory training applets which can capture MIDI and microphone input in-browser.
I could spend a year to rebuild what I can in JavaScript and HTML5 (there's nothing out there besides Java that'll give me MIDI input, of course), if I had a year to burn, which I don't.
Should I shut down the site entirely (and block thousands of users) because there are security issues appearing in OLD versions of Java, that many browsers don't even let you run anymore? Or should I just encourage browsers to keep refining their control over when applets can run -- so applets can be (again) simple to run by people who actually want them?
I'm leaning towards the latter.
The few who have to use it can keep using the old version and it being deprecated would put pressure on the websites that still use it to stop doing so.
EDIT: To elaborate on jokc's reply (who appears to be shadowbanned), it seems that this exploit is only a problem for applications that use Java's sandboxing features, and the browser plugin is the best example of this -- but desktop applications can use these features too.
Sandboxes only apply in the browser, as far as I can think of -- Java code all executes in the context of a security manager, but does anyone actually set a custom security manager for running untrusted Java applications? (Maybe I'm just missing an example you know of...)
A total nightmare from a security perspective.
They are starting to roll out a version for mobile phones now, but it requires that your operator supports it and many will need a new sim card so it takes time.
In the meantime if you are out with your friend and you finds out you want to see a movie, you will have to walk to the theater or call a friend with a pc to buy a ticket. You can't just do it online from you iPhone (some movie theaters may have a app for that, but not where I currently live :( ).
It feels especially bad because it wasn't always like this. Before the massive adoption of Bank ID you could do almost anything online from your phone.
Norway: https://www.bankid.no/
Sweden: http://www.bankid.com/
The Swedish one uses native apps for Windows, Mac and Linux rather than java. Still trivial to attack from a trojan though.. :/