Java applications are used a lot on the web. The smaller things like tic-tac-toe kind of games are irrelevant, but for example, Runescape is done in Java, and so are chat applications on some sites. IMHO, a device can't really claim to offer the full web experience without Java.

Consumer desktop applications tend not to use Java, but as others have said, many of us do use Java applications in a work setting. From my personal user's perspective, I really haven't witnessed poor performance. For example the RealVNC Java application has worked just fine for me. There's a longer wait when you start a Java application for the first time during your OS session, but even that disappears on subsequent use.