Lets discuss strategy/choice in a dungeon, and maybe even in PvP situations. Of course, this may vary based on personal builds and such, but overall...
(and not just healers should answer, I would love to hear everyone's side)
When Senche Tiger droppings hit the fan, and you, the healer, are about to die, but so is everyone else... who do you save? There is only 1 second to react, everyone is in view, but you know your next action will be your last (unless you heal yourself), and everyone needs healed... who do you heal?
Yourself? After all, what good are your heals if you are dead.
The tank? Chances are they will be the only one able to rez anyone.
That dodgy DD? Maybe they're the only ones in a safe spot, or have consistently been avoiding all the issues.
Now, this is very vague, but imagine one of your worst possible scenarios. Go!