This is the most common question I've heard from people choosing professions, and it's actually the easiest to answer. The fine folks theorycrafting on Elitist Jerks and other sites have done the math, and can answer that question definitively, so what I've done is compile that information, and condense it into a list format. I provide links for further information, and just a bit of explanation where I believe necessary.
Tanks
Best:Leatherworking - 710 Stamina (750 from Fur Lining minus 40 from Major Stamina). "750 Stamina is the same item budget as 1000 Mastery so even once you subtract the 170 [Mastery] you still end up at 830" - EJ.
Better:
Blacksmithing - 480 Stamina or 640 Mastery, Dodge, or Parry.
Jewelcrafting - 480 Stamina or 320 Mastery, Dodge, or Parry from 2 JC gems.
Alchemy - 480 Stamina from Mixology + Flask of the Earth.
Enchanting - 480 Stamina from 2x Enchant Ring - Greater Stamina. (Tooltip bugged to say 160 each, is 240.)
Mining - 480 Stamina from Toughness.
Good:
Inscription - 450 Stamina from Secret Ox Horn Inscription.
Engineering - 480 Dodge averaged. Phase Fingers gives 2880 Dodge for 10sec, 60sec cooldown.
I list Engineering lower because of Dodge's greater diminishing returns compared to Parry. For all tanks other than Druids, it is not one of the best options, but is still good. For Druids, the Parry/Dodge comparison is irrelevant, but Dodge still competes with both Stamina and Mastery.
Druid tanks may choose to stack Agility as it "Increases your Attack Power (threat), Dodge (survivability), and Crit Chance (threat + survivability)." - noxxic. Similarly for Monks, "Attack Power improves the mitigation of Guard and Crit increases the uptime of Brewing: Elusive Brew."- noxxic. In that case, follow the Agility options in the next section.
Strength/Agility DPS
Best:Leatherworking - 330 Strength or Agility. (500 from Fur Lining minus 170 Strength or Agility enchants.)
Better:
Engineering - 320 averaged. Synapse Springs gives 1920 Agi for 10sec, 60sec cooldown.
Blacksmithing - 320 Strength or Agility.
Alchemy - 320 Str/Agi from Mixology + Flask of Winter's Bite or Flask of Spring Blossoms.
Enchanting - 320 Str/Agi from 2x Enchant Ring - Greater Strength or Enchant Ring - Greater Agility.
Jewelcrafting - 320 Strength or Agility.
Inscription - 320 Str/Agi from Secret Tiger Fang Inscription or Secret Tiger Claw Inscription.
Good:
Herbalism - 480 Haste average. Lifeblood gives 2880 Haste for 20sec every 120sec.
Tailoring - 1,000 AP average. Swordguard Embroidery procs for 4,000 AP for 15sec every 60sec. Does not stack with 180 Crit or Hit enchants.
Skinning - 480 Crit from Master of Anatomy.
Intellect DPS/Healers
Best:Leatherworking - 330 Intellect (500 from Fur Lining minus 170 Intellect enchant.)
Better:
Engineering - 320 averaged. Synapse Springs gives 1920 Intellect for 10sec, 60sec cooldown.
Blacksmithing - 320 Intellect.
Alchemy - 320 Intellect from Mixology + Flask of the Warm Sun.
Enchanting - 320 Intellect from 2x Enchant Ring - Greater Intellect.
Jewelcrafting - 320 Intellect.
Inscription - 320 Intellect from Secret Crane Wing Inscription.
Tailoring - 320 Intellect average (500 minus 180 Intellect enchant.) Lightweave Embroidery procs 2,000 Intellect for 15sec every 60sec.
Good:
Herbalism - 480 Haste average. Lifeblood gives 2880 Haste for 20sec every 120sec. The self heal is 15-17k (125-141.7 HPS average).
Skinning - 480 Crit from Master of Anatomy.
Healers (Spirit Options)
Best:Tailoring - 900 Spirit average. Darkglow Embroidery procs 3,000 Spirit for 15sec every 50sec. Does not stack with 180 Intellect enchant.
Better:
Blacksmithing - 640 Spirit.
Good:
Alchemy - 320 Spirit from Mixology + Flask of Falling Leaves.
Jewelcrafting - 320 Spirit.