My rule (which I loosely follow, depending on mood) is that I try to read the text for new quests once, the first time I attempt that quest on any character. This has been especially true for the last 2 expansions where I was curious about the story and how it unfolds. It is doubly true for the phased starting areas such as Gilneas and Acherus.
I'm not a huge lore buff and I'm not one who likes to immerse himself deep into the story. I prefer to get right to the action (and that's one of the reasons why I prefer "mindless" action RPGs such as Diablo).
Sometimes the quest text is fun and worth reading. There's a particular chain of 2 quests in Mount Hyjal given by a dryad who asks you to save some "frightened rabbits and terrified squirrels" which is absolutely hilarious.
Most often, for me at least, the quest text is standard fare: "Kill 10 cockroaches" or "Bring me 10 rat tails".
Personally I can't wait to get the reading over with so I can go kill those damn rats.
What about you?