HotJava is the original Java application. It is (now) a mostly HTML 3.2 compliant web browser implemented in 100% Pure Java.
Unfortunately, HotJava is always one step ahead of the JDKs and JREs. This means that Sun issues it for Solaris and Win32, with the "purity" obscured by native scripts and wrappers. JavaLinux members have had some success getting the Solaris version running. Check there for details.
On a different slant, Sun's application setup for JavaOS uses HotJavaViews, a browser based UI.
On yet another tangent, Netscape and Sun recently publicized an agreement which gives Netscape access to HotJava technology for porting Communicator to 100% Java, thus accelerating that ongoing process by as much as a calender year(!). A version (beta?) should be ready by the time we start seeing Communicator 5 based products (middle 98).
HotJava is now on v1.1, available for all Java platforms that start with Windows or Solaris :(
v1.1 includes the HotJavaHTMLComponent, a JavaBean for HTML