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Check out SystemTray and TrayIcon. The latter can have an ActionListener or a MouseListener added to it to listen for click events; I believe that ActionListener is usually triggered upon double clicking, whereas with MouseListener you have full control over the number of clicks or even the button that was clicked.
You should always check if SystemTray.isSupported() returns true before using it; there's an example on the SystemTray Javadoc page.
