A triggered ability is controlled by the controller of the source of the ability when the ability triggers. Normally this is pretty straightforward. For example, with something like Blood Seeker the controller of the trigger is whoever controlled the Blood Seeker when creature came into play under an opponent’s control. In most cases the controller of a permanent is the controller of the card, however it is possible for a permanent to change controllers with something like Enslave. In these instances the controller of the Blood Seeker’s triggered ability will be its new controller. When this ability triggers will change as well, as who is considered the opponent is different.
With enters the battlefield triggered abilities the controller of the ability is the player that controls the permanent with the ability when it comes into play. For example, the controller of Squadron Hawk‘s triggered ability is the player that the controlled the Hawk when it entered play. (Keep in mind that when a permanent changes controllers it does not count as coming into the battlefield, so this ability will not trigger in these instances.)
Finally, equipment can be a bit odd. Sometimes equipment itself will have a triggered ability, other times the equipment will give a triggered ability to the creature that it is attached to. This can matter greatly, as it somewhat common for a player to ‘steal’ either a piece of equipment that is attached to a creature or the creature itself. (When a creature is ‘stolen’ the equopment that is on it will remain on it for now, but it will not change controllers.) For example, Sword of Feast and Famine has a complex triggered ability that triggers when the equipped creature deals combat damage to a player. One part of its ability affects the player that was dealt damage and the other affects the controller of the Sword. (All of the Swords from Scars of Mirrodin block are like this.) Things get tricky when a creature that is equipped by a Sword of Feast and Famine changes controllers and this creature attacks the original controller. Assuming that the Sword stays on this creature, then when this triggered ability resolves both parts will affect the same player. This means that the player that both controls the Sword and received combat damage by the equipped creature will discard a card and untap all of his lands.
Portions of todays rules tip were provided by Michael Jimenez a level two judge from Yreka, CA, USA.