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This could be achieved with plain CSS, depending on the behavior/actions you need to perform and if you don't need to support IE6.
If you need a client-server round-trip to trigger from the "mouseover" (e.g. need to validate some data that triggers the behaviour), you need to extend the server-side Window class and the client-side VWindow class and implement that functionality yourself using GWT.
If it simply a matter of showing or hiding some elements/components in the window depending on the "mouseover"/hover, you can use the CSS :hover pseudo class. If you need IE6 support, you need to extend the VWindow class and implement the hover behavior using GWT.
If you can provide more info of the use-case/behavior I can answer a bit more specifically.