Make your event handlers call a single function that performs the common functionality. You still have to wire up the event for each copied control, and Delphi's behavior might help there, but how often do you call the exact same code from multiple controls of the same type (there are other mechanisims for toolbar/menu duality)? You'll at least want to pass in different parameters or pull in information from a different set of other controls. Where do you put that code?
I guess what you and jbrabeck describe would save one extra copy/paste per copied control, but at the cost of having to erase that code for every control where you just wanted to duplicate the control's properties (ie: a row of buttons with the same size/color/etc).
Also, I didn't check earler, but in Access if you put an expression (ie: "=DoStuff" where DoStuff is a Sub containing your common code), in an Control's event property and copy that control, the text in the event property will copy much like Delphi's behavior.