Sun's Java Plug-in Updater – JUSCHED.EXE
Jusched.exe installs with the Java Plug-in by Sun Microsystems. This plug-in is needed to run Java Applets that you may encounter on the web if you use Microsoft Internet Explorer 6.0 or later as your web browser. As a result of a copyright infringement lawsuit by Sun Microsystems, Microsoft is no longer able to include its Java Virtual Machine that had previously been built into Internet Explorer.
If you're still running the Microsoft Java VM and you're also running the Sun Java Plug-in, Internet Explorer may crash. It is simply becoming confused by the multiple versions of Java. The easiest way to deal with this is to go to Explorer, click on Tools > Internet Options > Advanced then disable the Java VM. You'll find more information at http://support.microsoft.com/kb/555107.
Jusched.exe is the scheduler process of Java Update; Jucheck.exe is the process for checking/performing updates in Java Update. These processes run automatically and transparently. They will appear in your active task list when running. If you want to make sure that you have the latest version of the Sun Java Plugin, leave these files in place. Some prefer to wait until all of the kinks have been worked out of the latest version before upgrading. If that describes you, then you don't need these files. You can disable them via WinPatrol or you can simply uncheck the "Check for Updates Automatically" checkbox in the Update tab of Java Plug-in Control Panel.
You'll find Sun's available FAQs that cover all of Sun's J2, J2SE, J2EE and J2ME components at http://java.sun.com/reference/faqs/index.html.