System.exit(num) or throw a RuntimeException from main?

Don't throw an exception unless you really have an exceptional condition. System.exit(int) is there for precisely this reason. Use it.

EDIT: I think I may have misread your question. I thought you were asking, when you want to exit the JVM normally but signal that something did not quite go right, whether it is better to throw an exception or to use System.exit.

However, if the problem that occurs is something which is already indicated by a Java exception, it's fine to just let that exception go unhandled. You don't have to catch the exception and call System.exit.

If you have a choice of whether to throw an exception of your own or call System.exit, think about whether the error condition is something that might conceivably be handled by some Java code that calls your method. If the error occurs directly in the main method, then there will probably never be a caller to handle the exception so you should probably call System.exit. Otherwise, it's generally best to throw an exception - but not RuntimeException, you should probably use an exception type that appropriately represents the error you encountered. Write your own subclass of RuntimeException if necessary.

Generally in this situation I would handle all exceptions in my main method, possibly by calling System.exit. This gives you flexibility about where/whether/how to handle exceptional conditions, while still meeting your need to terminate with an error code. In particular, it gives you control over the return code and any other output you might generate for the user (error message, stack trace, etc). If you throw an exception in main (or let an exception escape), you lose that control.

To summarize, call System.exit only in your top-level exception handler:

static public void main() {
   try {
      runMyApp();
   } catch (Exception e) {
      System.exit(1);
   }
}

An exception thrown will print out the stack trace, and if you don't need that, you shoul use System.exit.

Upon exit you can inform the user with a Sytem.out (I assume the app is running in a commanline environment only).

You should consider just catching all errors an logging the errors in a seperate log, this ensures the stacktrace is not lost forever when you close the terminal. Take a look at log4j for this purpose, it's really easy to use.