A monster will attack you if you attack him first, if your threat is high to him and the tank is disabled, if you pull a "Leeerrrroy JJJenkins" stunt on the raid, if you heal someone while standing close to the creeps.

SO.

Here are a few ways i learned will keep aggro off you.

Healers - Ask a paladin to give you the BOS boost, it will lower your threat, making the monsters less likely to attack you. Stay away from the centre of the fight and heal from about 2 km away.
DPS - In case the tank is incapacitated, go towards the second tank cause chances are you will get attacked by the mobs. If the second tank cannot take the creeps off you, rogues should vanish, hunters, feign death, druids go into bear form, warlocks go to die away from the group so at least you buy some time XD.


Other info?

standard healer distance is 36 yards and make sure if your not a tank to get -threat talents