Well once there were class only quests.. which were long and hard (and mostly very expensive). Mount quest for paladin and warlock, and weaponquest for hunter and priest afaik. Oh and one of my favourite questlines was the epic flight form for the druid. I did all three with my main and two alts, I had many funny evenings with friends on TS while doing so.
The hunter one in Silithus was quite hard. I know quite a few people who got their quest done by a pro hunter on our server for gold.
I really would like to do a long quest again.. And by long I'm talking about really long. Like the food quest from Dirge etc.
A quest for all classes:
After quite a hard quest (maybe without hardcore HC raiding) you're able to transmog legendary weapons.
As for paladins:
A really long and hard questline where we get a replica of the Ashbringer (not the corrupted one, but a cheaper regular one) for transmog.
I know we're having that on one of our talents, but having it all the time would be epic. And the few lucky individuals who have the corrupted one from Naxx40 could still show their true rare weapon.
A quest for warriors:
Similar to the paladins questchain where they transform into a tank while in tank spec (those dwarven ones in front of Ironforge) .. na just kidding ^^
On a sidenote:
One of the things the old quests had in common was group questing. Many of the paladin mount quests had to be done in a group. I'd really like to have some quest dungeons where you have to go with 5x the class. The final one should remain a single thing like it was with the hunter & warlock green fire quest, but questing in groups is more fun.