The class quests are kind of a suck right now...afaik there's two for each class...one at level 20 and one at level 50...both of which are bland "go to this dungeon and kill the mobs there" affairs. They have absolutely no flavor. There's nothing class-specific about them. The point of a class quest is to do something that only you can do, or at the very least something that fits your class a bit more than "run a dungeon."
I've always thought that upon reaching max level characters should embark on a class quest. I feel that it makes very little sense that you're a hero of such renown that the Varian/Garrosh asks for you by name, and yet no one is asking you to do anything that specifically warrants a priest/warrior/whatever of your power? I mean...lets say you're a mage...perhaps you could be set a task by the Kirin Tor. Maybe there's a magically sealed vault in pandaria and they need you to join in casting circle to get inside, then there's puzzles or something inside that make you use your skills.
Also I would love if there were places like Moonglade/Ebon Hold/Peak of Serenity for the other classes, but they should do them Ebon-Hold-style where only that class should be able to enter.