I'm raid leader for my Kara team, and I found this the best stratagies:
For Attunemen, its pretty much a tank and spank. Our MT can normally hold both mobs, and we normally just burn down 1 of them. When Attunemen gets on his horse, we recommend that everyone gets fairly close to the MT, just to stop the mob from doing his charge interrupt on random people. We've had the horse drop twice from this guy. I just wish I were a little more lucky on the rolls.
For Moroes's adds, you need to look up what their skills are on wowwiki. You'll see 2 of the adds are healers, 1 will be a tankadin add, and the other will be a Warrior (with Mortal Strike). We have 1 tank on Moroes, and 1 off-tank for the tank add. We decide on a kill order.. where we kill the 2 healer adds, then the Warrior.. then Moroes. When Moroes dies, his garrote debuff gets taken off. I'd recommend having a priest & hunter for this fight.. just so you can kill the adds one at a time. Our guild has a 3-healer rule for Kara (as a safety measure), so I'm not sure if this method would work with 2 healers.
For Maiden, we have 1 healer that is on dispell watch. As soon as Holy Fire hits, it gets dispelled. Not much else to add here, but just to make sure that the healers have a line of sight on everyone.. and spread out during the fight.
For Curator, we put our team ( minus the MT) in a semi-circle or horse-shoe shape. We have all dps on the flare, and when the last flare comes, we have half-dps on curator, half-dps on the flare. Also using Seed of Corruption on Curator helps a little with the flares.
For Shade, we don't use a tank. We have shamans & rogues on interrupting duty for frostbolts and firebolts. We also have 1 experienced person making the ranged dps & heals move away from the Blizzard. Other than that, its not very difficult. We've had people move during Flame Wreath, and still managed to kill Shade. I do agree though, it is not pretty.
For Illhoof we have 2 Warlocks, 1 MT and a Warrior for OT. Seed of corruption is key for the annoying adds. We force our team to use a macro that targets the Demon Chains.. just so we can burn through it faster. We let the Warrior go nuts on Illhoof's demon, but we try to time it straight after someone has been in demon chains... so we have no interruptions on when we're burning down Illhoof.
I have nothing to add for Nightbane. A lot of people here have mentioned some sound stratagies. I just can't stress how important it is to move out of the charred earth. I have only downed Netherspite once, and haven't tried since. The mob is pretty difficult because of the timer, and a lot of my guild don't need anything from him.
I'm a MM hunter, and I never have my pet out for Prince's fight. We have killed him about 7 or 8 times in a row without wiping, but I'm putting that down to just pure luck with where the infernals drop. We have a rogue on our team that survives pretty much most of the fight, but he does run around lot when enfeebles hits.. hitting cloak of shadows.