Hitachi encountered this problem when they tried to shift their products from 1.3.0_0X to 1.3.1.
This problem doesn't reproduce on 1.3.0_0x older and other OS(Only windows).
Messages is following:
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D:\Hitachi\IO>java -version
java version "1.3.1"
Java(TM) 2 Runtime Environment, Standard Edition (build 1.3.1-b24)
Java HotSpot(TM) Client VM (build 1.3.1-b24, mixed mode)

D:\Hitachi\IO>java copy
set data to clipboard
java.io.NotSerializableException: my
        at java.io.ObjectOutputStream.outputObject(ObjectOutputStream.java:1148)

        at java.io.ObjectOutputStream.writeObject(ObjectOutputStream.java:366)
        at java.io.ObjectOutputStream.outputArray(ObjectOutputStream.java:1098)
        at java.io.ObjectOutputStream.checkSubstitutableSpecialClasses(ObjectOutputStream.java:456)
        at java.io.ObjectOutputStream.writeObject(ObjectOutputStream.java:361)
        at sun.awt.windows.WDataTransferer.translateTransferable(WDataTransferer.java:424)
        at sun.awt.DataTransferer.translateTransferable(DataTransferer.java:245)

        at sun.awt.windows.WClipboard.setContents(WClipboard.java:69)
        at data.initialize(copy.java:45)
        at data.<init>(copy.java:36)
        at copy.main(copy.java:13)
set data to clipboard OK!!

D:\Hitachi\IO>
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Test program is following:
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import java.awt.*;
import java.awt.datatransfer.*;
import java.awt.event.*;
import java.lang.reflect.*;
import java.io.*;
import javax.swing.*;
import javax.swing.event.*;

class copy{
    public static void main(String args[]){
try{
System.out.println("set data to clipboard");
new data(new my(), null);
System.out.println("set data to clipboard OK!!");
System.exit(0);
}catch(Throwable t){
t.printStackTrace();
System.exit(1);
}
    }
}

class data implements ClipboardOwner, Transferable{
    private Object source = null;
    private DataFlavor flavor = null;
    private ChangeListener change = null;
    private boolean invalid = false;

    static DataFlavor getFlavor(Class d){
return new DataFlavor(d, d.getName());
    }

    data(Object o, ChangeListener l){
Object[] array = (Object[])Array.newInstance(o.getClass(), 1);
array[0] = o;
initialize(l, array, getFlavor(array.getClass()));
    }

    private void initialize(ChangeListener l, Object[] o, DataFlavor f){
change = l;
source = o;
flavor = f;

Clipboard clip = Toolkit.getDefaultToolkit().getSystemClipboard();
clip.setContents(this, this);
invalid = false;
    }

    public void lostOwnership(Clipboard clipboard, Transferable contents){
invalid = true;
if (change != null)
change.stateChanged(new ChangeEvent(this));
    }

    public Object getTransferData(DataFlavor flavor) throws UnsupportedFlavorException, IOException{
if (invalid){
return null;
}else if (this.flavor.equals(flavor)){
return source;
}
throw new UnsupportedFlavorException(flavor);
    }

    public boolean isDataFlavorSupported(DataFlavor flavor){
        return !invalid && this.flavor.equals(flavor);
    }

    public DataFlavor[] getTransferDataFlavors(){
        return new DataFlavor[]{ flavor };
    }
}

class my{
    private String a = "aaa";
}
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