One part of Warcraft strategy lore I am not so sure about, however:
For pretty much any pull, you should follow the High Kill Order. It’s also known as the “Things That Suck to Tank” order.
Healers > Summoners > Gimmicks > Mages/Warlocks > Rogues > Warriors
Killing the healers is so ingrained that whenever the Straw Hat Pirates raid leaders tell us to attack a pack, they always call out over Vent, "Kill the healers!". Okay, they do this as much to annoy the healers in our own raid as anything, but still.
One part I'll agree on is that killing the healers first is the fastest way to dispense with a trash pack. The longer the healer is alive, the more damage must be healed through. Also, in general, ending the fight sooner has big advantages for survivability. Longer fights drain the healer mana and provide opportunities for everyone to slip up and get gibbed by some mechanic or another in the fight.
I started changing my mind about the "kill the healers" strategy, though, when Halls of Reflection came out in Lich King. In Halls of Reflection, there are several waves of 3-5 enemies attacking. The common wisdom for this instance is to first kill the healers, who are named, conveniently enough, priests. Yet, I've both tanked and healed this instance, and let me tell you: the priests aren't particularly annoying! What's annoying is that mage casting fireballs, that hunter casting frost traps, and that rogue that is blitting around and poisoning everyone.
I've come around to thinking that if you are having trouble surviving a trash pack, then you should kill a squishy, high-dps target in preference to a healer. Because the healer is alive, it will take longer to kill that high-dps target. However, once that first target is dead, you have significantly less incoming damage, and the fight becomes much more manageable. It's a more reliable way to get through a trash pack, though not a very common one.
To be sure, there are still times I'd favor prioritizing the healer. If you have enough gear that you aren't bothering with crowd control, then sure, kill the healer first so as to end the fight sooner. Also, as always, follow what the raid leader chooses. It's more important to single target *some* mob than to single target the ideal one.