Even more importantly, though, some packs of mobs put out too much damage for a tank and healer to control them all for very long. Killing one or two targets in a fast, coordinated way takes a lot of pressure off the need for heals. If you attack the entire pack at once using area of effect spells, then that pressure isn't relieved quickly enough.
Keep crowds controlled
Archmage Christian Belt has a wonderful primer about the basics of crowd control. Take the time to check it out, because it's one of the most important articles for Cataclysm. If you know nothing else about heroics or raiding, you should know this: love of Elune, just sheep something.
There are tricks to crowd control, of course. A lot of groups "sheep pull," trusting the tank to pick up all the mobs as they run toward the group. When you use this technique, it's especially important to give the tank a bit of time to grab the adds. That's because the mage actually has the initial aggro, and the tank will need the additional moments to get good control over the group.
Area attacks are risky
Be careful when using area attacks. If you've properly crowd controlled the enemies, then your area attacks could break that crowd control. Other, stray mobs might wander into the zone. While these accidents aren't insurmountable, they can certainly make your whole experience more risky.
Area attacks also have the effect of distributing your threat out among enemies the tank might not have fully controlled.
Run to the tank
Okay. So, accidents do happen. And when accidents happen, the mob will turn around and want to hit you instead of the tank. When that happens, go toward the tank. Don't run around, don't try and kite it, don't try and kill it super-fast. Just run it over to the tank.
Part of a tank's job is to maintain a boss in a stable position. Rogues have positional attacks, for example, and everyone has to pay attention to range. If a tank is moving a boss around the room, the group's collective damage will drop while it repositions itself to do proper attacks.
So if you're getting attacked by an add, run to the tank.
Give the healer time
Back in Wrath of the Lich King, healers didn't need to worry much about mana. Things have changed considerably. Many healers will find themselves without mana on nearly every fight. They will certainly be without mana within a few pulls. The only thing to be done about that is to let the healer have time to drink. Don't rush them; don't push them to "go go go." Give them time to drink, and everyone saves time running in from the graveyard.
Silence if you got 'em
It might seem pedantic to say so, but if you have a silence or interrupt effect, use it. Sure, some bosses have special effects that one-shot tanks, and you'll need to keep the abilities on reserve in order to use them at the right time. But aside from that, silence and interrupt everything you can. It saves an immense amount of trouble, and you'll find your group lives a lot longer when mobs can't cast.
Don't sweat DPS
There are many websites and forum posts dedicated to maximizing your damage. Don't get me wrong; doing the best you can is important. However, "the best you can" is not encapsulated entirely within the realm of DPS.
If you can interrupt a mob, crowd control during a pull, or debuff the enemy, that's worth giving up some DPS. If you can throw a heal on the tank to lighten the load, if you can stun an enemy for a moment, that tends to be worth giving up some DPS.
DPS is not the measurement of your success. Killing the boss is the measurement of your success. Cataclysm has more dance steps, and more complicated dance steps, than any other expansion. Take the time to get the dance for each boss correct. When you can cha-cha without thinking about it, your DPS will have caught up with you.
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to pulling together enough cash for mid-level expenses such as mounts, to dungeoneering and travel tips for lowbies.