Only a few dungeons are worth doing, while leveling. Also depends on your faction.
For Alliance, you'll definitely want to run Deadmines once, not only because there's a good handful of quests in there, but because it starts a long quest chain that gives a lot of exp and a nice ring.
-Quest item off of Sneed
-Quest chain that ends in quest to kill VC, and then the follow-up from the looted item which starts another quest chain
-Quest to get the red silk bandannas
-Quest to kill the elite in the mines just outside the instance
-Quest to get the miners' cards from the other elite undeads in that same area
Good amount of EXP to be had there.
Stockades can be nice as well, as it can easily be completed in 30-45 minutes, and there are 4 or 5 quests to kill the various named elites in there. At level 27/28, the quests + full clear of the instance should net you around 50-60% exp, for that 30-45 minute dungeon run. Noice.
Zul'Farrak is another dungeon that has a shitload of quests, and almost all of them are easy to get, as they're right in Tanaris/Shimmering Flats.
In general, skip dungeons unless you've got at least 4 quests there.
For reference, I leveled my Priest doing every single dungeon at least once (except RFC / WC) and it took me a little over 9 days /played to hit 60. On my Hunter however, I completely skipped all dungeons (except ZF) and I'm at 52 with about 4.5 days /played. Big difference, as you can see.
Blazeforce wrote:I'm just wondering what the viability is of lvling strictly by running dungeons and not actually doing quests other than the ones that are directly associated with dungeons?
Not very viable, imo. Dungeons give pretty shit exp, since the mob kill exp is shared between 4 other people. The lower dungeons like Deadmines, SFK and Stockades will give *decent* exp, but I found that the higher level you go, the less exp you get from dungeons.
Don't level "strictly by dungeons" unless you love monotony and have a LOT of time on your hands.