Check the Java Console - it probably contains error messages. In particular, calling Runtime.exec is not allowed in applets unless they are signed or the local security policy has been altered. See HowCanAnAppletReadFilesOnTheLocalFileSystem for more details.
Could be all kinds of things. Perhaps your code makes some assumption about the current working directory when Runtime.exec runs. Perhaps you're trying to run an executable which isn't on the computer where the applet runs. We could make a longer list but there isn't any point.
Are you getting an exception from Runtime.exec? Don't just say "it doesn't work", find out why not. Look at the Java console in the browser for a start.