Gandalf the White

You don't need to control the permanent entering or leaving the battlefield, only the permanent that has the triggered ability.

Abilities that apply "as [this permanent] enters the battlefield," such as choosing a color with Gauntlet of Power, are also unaffected.

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.

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."

Replacement effects are unaffected by Gandalf the White's ability. For example, a legendary creature that enters the battlefield with one +1/+1 counter on it won't receive an additional +1/+1 counter.

If a legendary permanent or an artifact entering or leaving the battlefield at the same time as Gandalf the White (including Gandalf the White itself) causes a triggered ability of a permanent you control to trigger, that ability triggers an additional time.