Yes. In general see http://www.mathworks.com/help/matlab/math/parameterizing-functions.html
However, in the special case of setting up callbacks, when you use the cell syntax like you do in 'Callback',{@button_Callback} then anything you put as additional cell elements will be passed as an additional parameter to the function. So for example if you had 'Callback', {@button_Callback, i} then the value of i as of the time the control is built, would be passed as the third parameter to button_Callback so you could know the button number.
However... even that turns out to be unnecessary. When a callback is invoked, the first thing passed to the callback is the handle to the object that the callback is about. So even with just 'Callback',{@button_Callback} the first parameter passed to button_Callback would be the handle to the uicontrol, same as what would have been stored into mybutton(i) . You can use that to access the uicontrol properties, including the String property, or including any UserData that you might have set when you built the uicontrol.
