Sometimes. Depends on how the buttons are wired in the appliance. Ideally you'd get/make a schematic of it, or alternatively do some measurements and second-guess it.
Another option is to use relays; this is generally easy (electrically at least) and is virtually certain to work regardless.
Will it be sufficient for the Arduino to press buttons or does it also have to read displays etc? That would complicate matters enormously.
What kind of appliances are we talking about and what sort of actions do you want the Arduino to perform on them?