How To Not Pull Threat

A very real danger to any DPS class is the risk of pulling aggro from your tank, and thus getting yourself horribly squashed, and potentially wiping the party.
If you have mad DPS, but keep pulling aggro and getting killed 15 seconds in, you are useless. Worse than useless, you are a liability to the party.

Don't be the warlock who opens each fight with a Shadowbolt crit of 4k.

Don't be the Boomkin who starts off every boss fight with a Starfire crit.

And please, for the love of all that is Mageness, don't be the mage who fires off PoM + Pyro the same second the Paladin first hits the mob.

So, here are some strategies on mitigating threat, and how to work with your tanks to avoid being a dumbass.
You may not always be able to avoid threat, but you can mitigate it.

1. The most obvious way to avoid pulling aggro is to put points into whatever talent reduces the threat your spells do. For Arcane, its Arcane Subtlety (40% reduction), Fire mages have a 10% reduction through Burning Soul, and Frosties have a 10% through Frost Channeling. There is no reason not to get these talents, and the Fire and Frost versions are painful to go without.
   
2. Give your tank a little bit of a head start. If there is a hunter in the party, misdirect will give your tank a huge boost to their threat, but it still won't be enough if you drop three crits in a row right off the bat. As Arcane, ease slowly into the fight with Arcane Missiles, and ramp up from there. Does AM hit hard? Why, yes, it does. But, as a channeled, its threat is more spread out than any other Arcane spell. An excellent opener. As a note, though, the Arcane tree has rather low innate threat, so you can simply open as normal with Arcane Blast. As a frost mage, don't worry about it. Chances are pretty good frostbolt won't cause any problems, and if it does, well, the target is slowed and so easily controlled. You can Ice Block twice as much as anyone else. If you do ever run into aggro issues, ope with an Ice Lance or two to start the crit debuff with generating practically zero threat. As Fire, open with Scorch. Scorch does not produce a lot of threat, even when it crits, and has an added perk that practically requires you to open with it. The whole increased fire damage thing? Yeah. You gimp your own damage if you don't have that at max debuff at all (or almost all) times. If there is still aggro issues with opening with Scorchx5, then downrank. Rank 7 works very well for avoiding early aggro, and has the added bonus that it still tossses up the debuffs. Wait to use fireballs for at least 10 seconds.
3. Get an enchant. A new enchanting formula for your cloaks and capes reduces all threat by 2%. Far, far better than the 20 Spell Penetration alternative... unless you're one of those kinky mages who likes Agility.
4. Don't be afraid of using Invisibility when it is needed. Whatever threat you have, it cuts it in half. If you use it around midfight, or a little earlier, it effectively means that it is impossible for you to pull aggro, no matter what you do. Take, say, Mechano-Lord Capacitus in heroic mode as a fire mage. Full Scorch debuff, then fireball away, and let the crits flow. When you hit about the 110% aggro mark of the tank, hit invis, let 6 seconds go by, cancel it, and keep right on fireballing. You'll be at the bottom of the threat list, blasting out thousands of damage in a single fireball.
5. If you suddenly snag aggro, Ice Block. This option will become avaliable to any and all mages soon, and its an instant aggro dump. You get all that threat back, however, but its ten seconds where you were doing nothing and your tank was furiously getting aggro back. However, don't dump the aggro on the poor Holy Priest next to you. That's just uncalled for. Dumping aggro in the Hunter next to you is acceptable.
6. Do something else. Mana running low? Evocate. Took some AoE damage in a fight like Grandmaster Vorpal or Thespia? First-aid yourself. An add pop up that needs to be taken care of? Sheep it if you can. Healer suddenly pull aggro from a flesh monster thingy in Arcatraz? Take care of the situation, and save your healer and tank a helluva headache. The latter option is especially good for frost mages. A non-elite mob that can be rooted? /scoff
7. And above everything except #1, KNOW YOUR TANK. If its a Warrior, give them a bit to get at least one or two sunders up before you damage the mob at all. Same with druids, except its called Mangle or something. It looks like a little slashy mark on the debuff bar. In the case of a Paladin, you can start right away, but start low. Use a downranked spell a time or two. In the case where multiple mobs are being tanked, Warriors are the most sensitive here. Do not attack ANY mob until the warrior has put at least two sunders on it. Again, same with druids. Paladins it doesn't matter too much, so long as you let Consecrate do its work for a bit. A good rule of thumb: on the main mob, let about 8 seconds of continuous casting go by on the main mob. Fire can judge this the best, as the perfect time is when Scorch reaches max debuffs. Then, unload with some AoEs. Flamestrike, Blastwave, Dragon's Breathe, whatever, you'll be good to go. Paladins are the best AoE tanks in the game, revel in it.
8. Get an addon that shows people's threat levels. Omen is arguably the best one out there. It's pretty, full customizable, it keeps track of aggro on multiple mobs, and is backwards compatible with threat meters like KTM.