The quest-line that leads up to The battle for undercity, the one in icc with Matthias Lehner that leads up so you fight Illdan as Arthas when he's a DK, pretty epic. (As Horde)
I also loved the first time I did the quest-line in Nagrand so Thrall came to pay a visit.
The absurd carapace farming actually sucked big time but after that it had really nice stuff to see and do.
Finally holding ready Scepter, banging the Gong and starting to beat Anubisaths with your buddies and hundreds of others in the realm
AQ scepter quest was by far the best questline in the game. Nothing in BC or WOTLK compares.
Hunter Rhok'delar Bow quest was also a very challenging questline. I think doing this quest was one of the hardest things I have done in WoW.
Getting attuned to the Black Temple was a pretty cool quest line as well.
Edit. the part of the Wrathgate pre-quest where you have to get the emerald dragon tears, the forsaken in the lab has a very dry sense of humor...
"With an inert specimen of the blight compound complete and the activating agent in hand there only remains a need for a suitable shell to house the components.
Southwest of here, on the shores of central Dragonblight, is where you will find the Emerald Dragonshrine. Within the shrine you will find the hardened remnants of a green dragon's tear drop. I don't know the whole story, but apparently they cry a lot right before they die. Go figure."
1. The Darrowshire questline (The whole Pamela thing)
2. The questline from The fallen hero of the horde (or smth)
3. The quests for The Scepter of the Shifting Sands
4. The questline that starts with the Greatmother in Nagrand
5. The line required for Champion of the Naaru
1. Druid Flight Form (with river chase!)
2. Greatmother Nagrand
3. Sons of Hodir attunement
4. Scalawag Point/graverobbers quest
5. Guru of Drakuru
6. Path of Conquest (Shadowmoon)
The Priest class quest The Balance of Light and Shadow.
At 60 and without help it sure was a pain in the ***, but it gave a very nice flavour to the priest class.
The questline where you fall through the floor under ICC, you meet a little boy who you eventually come to find out is arthas, or some part of him. You go through and kill soldiers, fight illidan, and quest with tirion to steal the Lich Kings heart, the sheer awesomeness of it made me not want it to stop, if you haven't found this quest, you need to.
For the reward and the very manly tears it's a split between The Crusader Bridenbrad questline or Peace at Last http://www.wowhead.com/quest=11149 which is short but has a rewarding end. The Sons of Hodir quest chain beginning with http://www.wowhead.com/quest=12843 was a memorable one, mainly for the Indiana Jones style Drakkensryd sequence but also the final fate of Thorim and Loken. It's one of those rare quest lines like the Drakuru chains where you're reminded 'there's always something cleverer than yourself'
Two of my favourite quests are also class only sadly; the level 20 warrior quest http://www.wowhead.com/quest=1699 is simple but fun; get drunk and up to the mouth of a cave full of knolls without dying for a dare, and the end script of the warlock infernal quest which has some demented gnome summon a giant black chicken to try and kill you followed by the immortal words 'Silence, servant! Vengeance will be mine! Death to Stormwind! Death by chicken!'
There's also a poem you have to deliver to a child in the Aldor section of Shattrath; I do not recall what it is but reading the story behind it made me, for a few moments actually appreciate the people who take time to add these little gems to the game