Id have to say the top of my list has to be Crown of Earth and the Fishing Quest in Auberdine.
Crown of Earth has you running all over Teldrassil filling vials in moon pools and returning to a Druid in Dolanaar. Its a four stage quest thats results in a quest to kill the boss Ursal the Mauler, I believe. Its really good xp for the level. It uncovers alot of the 6-10 map area for you. It also has a bit of stealthy gameplay as you can try to avoid higher monsters surrounding the pools near Darnassus and the Oracle Glade.
The Fishing quest in Auberdine is another unusual and non violent quest that gets people started into fishing. All you have to do is catch 6 dark shore groupers and youll prolly be around 15 in fishing, get a nice magical fishing pole and some good experience and a few silver. (edit: read anti grind quest)
I also like the Goldshire quests where you have to find Bernice's locket by killing boars to make a meat pie for Billy, the guy who stole it.
Another great quest in Goldshire is the quest to reunite the lovers of the opposing farms by making the invisibility potion. I could have sworn the potion would turn out to be poison but I guess they wanted to keep the Teen rating...
Molly's collecting grapes in the vineyard quest is neat. ANother one along those lines is the Undead area's collecting pumpkins. The latter is especially evil since the quest giver spices up the pumpkin to turn a captive into and undead minion!
OMG, how could I forget the Buzzbox series and the capture the rabid thistle bear quest in darkshore. Those are terrific!