One of my personal pet peeves is that DPS (damage-dealing) characters are judged solely on the number they put out. Admittedly, some of this peevishness comes from the fact that one of my 70s is a shadow priest, the ultimate in auxiliary usage -- but people actually do seem to appreciate shadow priests a lot, and I haven't found myself often turned away because someone wants more DPS. But it's not just shadow priests -- in fact, I would argue that in a raid setting, or even more so in an instance setting, intelligence trumps damage (and especially, trumps gear.) If you really want to be a successful DPS instead of just a high-damage one, every class has things they can do to really help out the group:
Hunters: Misdirect is one of the best spells in the game. Use it well. Here are some ways you can use it effectively: at the beginning of a pull to draw enemies to the tank or ramp up the latter's threat quickly (especially good with a warrior/druid), to get enemies off the healer (you'll want a macro for this), and to reestablish aggro after an aggro wipe (a specialty of many hard bosses.) A good misdirecting hunter will make everything a hell of a lot simpler. Also useful: good pet off-tanking, and of course good trapping (especially emergency/caster trapping.)
Mages: Here's a nice move that requires some coordination: if a mob is on the healer, frost nova it, and have the healer step away. Inform your healer than you may do this. Of course, good sheeping is important, but pretty easy to do for the most part.
Warlocks: Keep that soulstone up! The number of warlocks who don't do this is baffling. Other than that, you have a fear and a banish -- use them effectively to control panic situations. Obviously the former is a double-edged sword, but a well-timed and -placed fear can prevent a wipe just as easily as a poorly- one can cause one. Banish is the only crowd control in the game not broken on damage: don't be shy.
(retributive) Paladins: Cleanse. You have the best anti-debuff spell in the game; use it. Wake up people who are asleep. Nullify noxious poisons. The healers have their hands full with damage a lot of the time; don't be afraid to help. Because of your gear, you won't be a great offhealer, but occasionally you will see a chance, and of course there's always Lay on Hands. Divine Intervention is there for wipe protection, but every paladin worth their salt should be familiar with this. Finally, Hammer of Justice and Blessing of Protection are there to defend your healer. Use them. Hammer is also underrated at preventing damage spikes at the beginning of pulls. A 1-minute cooldown means that it need not be a panic button; use it early and often (but, of course, not befre the tank has placed the fight.)
Rogues: Stuns are the main tool that can be used for great good or great evil. Tanks hate nothing more than to see you open with Cheap Shot before they have aggro on the target or before they place the fight (especially true for paladins.) On the other hand, see that caster who isn't coming into the fray? Go over to him and stunlock him or kick him and bring him in. Between kicks, gouges, and stuns, any rogue should be able to solo a normal at-level instance caster. Your abilities are ideal for neutralizing these types -- for instance, a second non-crowd-controlled healer is a huge danger -- and you shouldn't necessarily wait for the tank to instruct you to do so.
Shamans: Earth shock, earth shock, earth shock (free tip: rank 1.) Also, choosing the right totems to help your group out the most (instead of, perhaps, just you) makes a big difference, and keeping them up will ultimately prove to be a win for your side, even if it means sacrificing a bit of DPS. Obviously, some offhealing helps, which elemental shamans are better at by virtue of gear.
Warriors: Disarm! Even many bosses (e.g. Attumen the Huntsman) are vulnerable to this trick, which your tank will thank you for. Also, consider using Commanding Shout instead of your usual Battle Shout, depending on the fight. Finally, some sunder armors on the target may work wonders depending on group composition. If you aren't a particularly threat-generating person, drop some sunders on and watch the boss's health bar dwindle. In caster boss fights (e.g. Shade of Aran), don't be afraid to strap on a shield and interrupt using Shield Bash. Really.
Druids: Druids are blessed with amazing in-combat versatility. Something on your healer? Consider going bear form. Healer down? Switch to caster form and start healing (with some changes to the feral combat tree, cats are now better at this than before.) The cat is actually in a fantastically versatile position: because their normal ability doesn't use mana, when they pop over to heal, their mana bar will be nice and full. You can dump this mana tank and then promptly switch back into cat. It's a very nice benefit to the group. Of course, the X factor in many fights is the druid's battle rez: using this well (perhaps not rezzing a DPS in case a healer goes down, or perhaps just being twitchy) will often give your group a much larger margin of error. Finally, Cyclone is certainly underused, both as a healer defense mechanism and as a mitigation tactic.
Shadow priests: Shadow priests have some amazing features. Of course, they can pop out of shadow form to offheal when necessary (try a Prayer of Mending pre-pull, too), but even more amazing, they can cast Power Word: Shield while in shadow form. Do not underestimate this -- I can't tell you how many wipes I've saved by popping this button, giving a 1500-2000 hp buffer while the healers catch up. Aside from maybe misdirect, I think this is the single best non-dps, non-crowd control spell available to damage-dealers. It's an instant cast, of course, which is huge. Aside from this, dispel magic, like with the paladin (although not quite as powerful), is a nice tool to help out. Finally, you have the fear, to be used only in emergencies, but a nice way to save your healer out sometimes.
The problem with this, of course, is that you can't very well tell whether Joe Druid who is messaging you will be good at this or not. You can check out his gear on the Armory, but you can't tell if he will be a good offhealer on instinct, or how his bear reflexes are. Maybe with the achievements coming in WotLK you will be able to check out his success in past endeavors, but I wouldn't count on it. So, ultimately, these skills won't help you get into PUGs, and if you are with a particularly blind group who just checks damage meters, won't help you make friends. But those probably aren't the kind of friends you want anyway. So, be a better player: maybe a bit less damage, but many fewer wipes, and a nice experience for all.