The reason the connection to the signal does not work is because you are using the wrong signature for QListWidget.itemDoubleClicked . It should look like this:
self.connect(self.listWidget, QtCore.SIGNAL("itemDoubleClicked(QListWidgetItem *)"), self.showItem)
However, I would advise you to avoid using this altogther signal hooking method and switch to the new style syntax instead. This will allow you to rewrite the above code as follows:
self.listWidget.itemDoubleClicked.connect(self.showItem)
Which is not only simpler and cleaner, but also much less prone to errors (in fact, if an incorrect signal name / signature is used, an exception will be thrown).