Excellent, excellent information in the replies so far.
I'm new to shaman healing; I came from healing as a Disc priest. The healing forum (here) is a great place to get advice, but the Priest forum is also an amazing class resource for you. No need to pick one over the other; just know that both are good resources for you :)
The advice I'll tack on is as follows:
When you *do* get a tank who's insistent at running the instance at warp speed, the key is that everyone needs to move along with him. He will stop running when he's pulled everything he wants to pull; he left it in the dust because so long as no dps hit it too much, it will stay aggro'd to him, and it *will* chase him until it catches up with him.
If the dps'ers don't realize this, they will stop to try to kill things (usually casters, since caster mobs don't pull as fast as melee mobs). Eventually, they'll put enough damage on the mobs that the mobs will aggro to *them*. Except your dps'ers haven't continued running with the tank; they stopped to kill the mob. Now the tank has no way of re-establishing aggro on the dps.
New healers (or even experienced healers who intensely dislike tanks pulling like this) make the mistake of hanging back with the poor, lagging-behind dps to try to save them, and then try to catch up to wherever the tank is, hopefully in time to heal him up if he's managed to round up as many mobs as he'd wanted to. You may be lost, by then, though, in some dungeons.
The ideal thing to do in the situation of a tank who's hellbent on pulling multiple trash packs is for *everyone* to keep up with the tank. The rogue, the hunter, the mage, *and* you. Don't stop until he does. No one should dps *anything* until the tank stops. Once all the mobs have caught up, dps can start AoE'ing their butts off with little worry of grabbing too much aggro, and you can focus on healing the one person taking the majority of the damage - the tank.
Now... this falls apart if the tank doesn't know how to tank, and thinks all he needs to do is collect a bunch of mobs and hit them with random abilities. Also, at extreme low levels, some tanks have trouble keeping threat on a group of targets. But most of the time, it's a winning strategy.
Sometimes, I'll hop into a 5man on one of my lowbie alt healers, and the tank will be pulling like crazy, and the dps will not understand that they need to stay with the tank. If the tank hasn't said anything, I'll say "hey guys, I'm going to be sticking to the tank like glue. Just keep running with us, and you'll be in range for heals if you end up needing them. Don't worry about the mobs chasing us - so long as you don't dps them until our tank stops to fight them, they'll be completely aggro'd to him." That often helps.