java version "1.4.0-beta"
Java(TM) 2 Runtime Environment, Standard Edition (build 1.4.0-beta-b65)
Java HotSpot(TM) Client VM (build 1.4.0-beta-b65, mixed mode)

Frames can be programmatically maximized with
setExtendedState() but only after having being shown,
otherwise they are shown in normal state, as the sample
code shows.
The workaround is to first show the frame, then maximize it.

//--------------------------------------------
import javax.swing.*;

public class Maxim extends JFrame
{
 public static void main(String args[])
 {
  new Maxim();
 }

 public Maxim()
 {
  setDefaultCloseOperation(EXIT_ON_CLOSE);
  setExtendedState(MAXIMIZED_BOTH);
  show();
 }
}
//--------------------------------------------
(Review ID: 125293) 
======================================================================

//--------------------------------------------
import javax.swing.*;

public class Maxim extends JFrame
{
 public static void main(String args[])
 {
  new Maxim();
 }

 public Maxim()
 {
  setDefaultCloseOperation(EXIT_ON_CLOSE);
  show();
  setExtendedState(MAXIMIZED_BOTH);
 }
}
//--------------------------------------------
======================================================================

Windows part is resolved (see evaluation and suggested fix for 4464710), but on
X11 this is still impossible.
 xxxxx@xxxxx  2002-09-03

The user can see the app being painted first in normal 
mode, then expand to maximized (using the workaround). It's 
very unsightly, and the initial user impression is that 
every disparaging remark about client-side Java is true. 
For us Java application developers this is a critical bug 
to fix because first impressions are very important. Please 
don't sell us short by not fixing in a timely fashion such 
a critical bug. This affects user acceptance of our 
applications.

import javax.swing.*;
public class MaximizedWindow extends JFrame {
   public MaximizedWindow() {
      // Add stuff

      // Realizes the frame but does not show it
      pack();
      setExtendedState(MAXIMIZED_BOTH);
   }
   public static void main(String args[]) {
      new MaximizedWindow().show();
   }
}

The problem really stems from the Frame not having been 
realized. This is done by calling setVisible(true), show
(), or pack(). After the frame has been realized you can 
maximize it.

Great catch on using pack() as a workaround before calling 
setExtendedState(JFrame.MAXIMIXED_BOTH). 

If this still isn't fixed under X11, why is the bug closed??

It is still not working under Windows XP JRE 1.5.0 and 1.6.0, if you set the content pane. You can reproduce it with this example by adding the line setContentPane(new JPanel()) in the constructor of Maxim. This bug should be reopened.