Hand of Sacrifice can be used to avoid being the victim of Crowd Control in PvP. Bless a person who is quite likely to draw enemy fire. This way, if you're afflicted by Polymorph, Sap, Repentance or any other incapacitating effect, the damage transferred to you would break Crowd Control.
Hand of Sacrifice can be useful in PvE when tanking mobs that fear in 5-man instances, such as the Fel Overseer in Shadow Labyrinth. If you put Hand of Sacrifice on a party member you know will not get feared, them getting hit will break your own fear.
Hand of Sacrifice can be very helpful when tanking Blackheart the Inciter, especially during his 'incite chaos' spell to take damage away from all party members, and also for picking him up after his 'incite chaos' spell wears off.
Critical during the Maiden of Virtue fight in Karazhan, allowing paladin healers to be awake during the Maiden's Repentance. All of the paladin healers should keep Hand of Sacrifice activated on the tank and melee DPS. Decide before the fight on who to bless whom, as it cannot be cast on the same player by two paladins.
Note that using Hand of Sacrifice may make it difficult for the healer to heal. Normally, the healer would only need to heal one target. Under Hand of Sacrifice, both you and the player you blessed would take damage. Be sure to communicate this to the main healer, and do try to heal yourself from your own mana pool if it is feasible.
During the fight against Maexxna in Naxxramas, if everyone is about to get hit by the Web Spray effect and Maexxna is Frenzied, casting Hand of Sacrifice on the main tank will help him or her survive.