What is the ooze priority for Yor'sahj the Unsleeping?

Solution 1:

My guild actually does the opposite order of the other answer.

1. Green
2. Yellow
3. Purple

We stay stacked up the entire fight when not killing slimes. Purple is only dangerous if more than the tanks need to be healed. Don't use aoe heals and assign one healer per tank (if you are using two) we use two in our 25 man to make tank healing easier. Have those two healers only use big heals and only when necessary. If you must make the tank blow up make sure they have enough health to survive and it shouldn't be a big deal. We have plenty of dps without needing to go with one tank.

As mentioned in the other answer, when you get Yellow, Green, and Red (The most dangerous combo) kill Green Always! That way you can stack up and use raid cooldowns to survive the phase. The healing lead asks for each players cooldown as needed.

A lot of players are scared of Purple, and I admit, in the raid finder, Purple will probably always be the most dangerous. That is because you cannot communicate healing assignments as easily. In a normal mode, with voice communication and a good group of players, Purple is easy to deal with.

Solution 2:

The first priority is always purple. No questions asked. If purple spawns, kill it. If the purple ooze does manage to reach the boss, it grants him the Deep Corruption ability. With Deep Corruption up, each direct heal or damage absorb will grant a stack. At 5 stacks it explodes, pretty much wiping the raid.

The second priority is yellow, because it causes the boss to do a ton of extra damage. Void Bolt becomes an AoE, his abilities refresh twice as fast, and gains 50% increased attack speed. This is very hard on the healers.

Third is green. If the green ooze reaches the boss, it causes each player to emit AoE damage in a short radius, which means spreading out. However, other mechanics in the fight requires stacking up (for healing, to kill adds, etc). When you are trying to spread out and stack up at the same time, things get messy and raids wipe.

_{Note that the second and third priorities are not set in stone. Some groups may swap them, especially as healers start to gear up in Dragon Soul and can handle the extra damage from Yellow more easily.}

There is one notable exception to the priorities above.

Yellow, Green, Red
When these three oozes spawn, things are about to get dangerous. If Green and Red hit the boss, you have to group up and spread out at the same time. For obvious reasons this doesn't work too well. You are forced to kill Green. But now you have to deal with Yellow and Red, another painful combination. Get ready to pop some cooldowns.

So to summarize:

1. Purple
2. Yellow unless Green and Red are also up
3. Green

Note that these considerations are for a raid leader who has to make quick decisions when the oozes spawn. If you are not the raid leader, kill the ooze that is called out or marked, regardless of any priorities you think are correct. It's better to have everyone working together instead of arguing or splitting the DPS and having to deal with 3 abilities (4 on heroic) at once.