Gandalf the White

The trigger event doesn't have to specifically refer to legendary permanents or to artifacts, nor does it have to specifically refer to when something "leaves the battlefield." For example, an ability that triggers "whenever a creature dies" would trigger twice if a legendary creature or an artifact creature dies while Gandalf the White is on the battlefield, as would an ability that triggers "whenever a permanent is put into a graveyard from the battlefield."

Gandalf the White affects a permanent's own enters-the-battlefield and leaves-the-battlefield triggered abilities as well as other triggered abilities that trigger when that permanent enters or leaves the battlefield. Such triggered abilities start with "when" or "whenever."

If you somehow control two copies of Gandalf the White, a legendary permanent or an artifact entering or leaving the battlefield causes abilities to trigger three times, not four. A third Gandalf the White causes abilities to trigger four times, a fourth causes abilities to trigger five times, and so on.