Regardless of the Java VM you're using, from time to time you'll encounter a client that is unable to run your applet because of an "undefined package" error, even though the package involved is part of the standard Java distribution.
The most likely culprit in this case is the Java "ClassPath" setting. For the Sun JDK, this setting is implemented as an environment variable, and you should be able to quickly check if it actually points to the right directory (the one containing the file "classes.zip"). The Microsoft VM makes this setting a bit harder to find: you'll have to go into the Registry Editor and check the ClassPath value stored in the key HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Java VM.
If the ClassPath setting seems to be correct, you might try replacing classes.zip with a known-good version, but due to version differences it's probably best just to re-install the latest version of the VM you're using. The Sun JDK can be downloaded from the Web at http://java.sun.com/products/jdk/, the Microsoft VM at http://www.microsoft.com/java/.