You could create a small draggable Applet ([Java Tutorial: Draggable Applets|http://java.sun.com/docs/books/tutorial/deployment/applet/draggableApplet.html]) and just return true in the isAppletDragStart(MouseEvent e)-Method. Then you could set the JApplet (or, if this doesn't work, use an undecorated JFrame) to be always on top and position it somewhere on the screen, maybe on the title bar of the browser. Then it doesn't matter which pages the user visits.
It's not a toolbar.
I don't know how you could determine when/if the browser gets minimized/closed (But the JVM knows when the browser gets closed).
Only Sun's JRE supports it, since JRE 1.6.0_10.
That's all I can tell you. Maybe you could do something with the Java Native Interface to put it into a browser, but then you can't use e.g. Swing.