Vanilla: The original Duskwood. It was my favorite zone with my favorite stories, in particular the Morbent Fel chain.
TBC: Hanging out with Khadgar's servant.
Cata: I don't remember if the quest chains intertwine but Cata introduced a new/updated series of pirate quests to STV that were a blast and I really dug the chain that culminates in the defense of Booty Bay. Fiona's Caravan is a good one. I thought Vashjr was effective in setting up a story that felt bigger than you, what with all the Old God and Naga civilization stuff.
MoP: The Alliance chain in Jade Forest starts off a little shaky in the intro quests but it actually becomes pretty engrossing and funny. Highlights off the top of my head would be painting the mural, the Jade Witch, and the SI:7 stuff. The short Hidden Master chain in Valley is great. Bad yak.