For Dwarves, I was thinking maybe a passive increase on armor of 2%, which would go well with Stoneform. Lofty's idea of increasing race's professions skill points is a good idea too, though I always saw Forsaken as being alot better at Alchemy. But I also see Goblins as getting +alchemy as really odd, as I thought they would get +engineering, even if that would put them at odds with gnomes.

Gnome Racials:

*Escape Artist – Instant – 1.75 min cooldown
Escape the effects of any immobilization or movement speed reduction effect.

*Expansive Mind – Passive
Intellect increased by 5%.

*Nimble Feet – Passive
Agility increased by 5%.

*Arcane Resistance – Passive
Reduces the chance you will be hit by Arcane spells by 5%.

*My Little Gnomie – 30 min cooldown
Summons a personal Gnomie™ repair-bot. Repairs items at half the normal cost.

*Engineering Specialist – Passive
Engineering skill increased by 15. In addition, many engineered devices have a greater chance of working as intended.

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Undead Racials:

*Will of the Forsaken – Instant – 2 min cooldown
Activate to remove any fear, sleep, and charm effects.

*Life Leech – Passive
Returns 2% of all damage or healing done as health.

*Reanimate – Instant – 30 min cooldown
Return from the grave after a death. (Only usable outside of combat.)

*Cannibalize – Instant – 2 min cooldown
Activate to regenerate 10% of total health every 2 seconds for 10 seconds. Only works on Humanoid or Undead corpses within 5 yards.

*Underwater Breathing – Passive
Underwater breath lasts 233% longer than normal.

*Shadow Resistance – Passive
Reduces the chance you will be hit by Shadow spells by 5%.

*Master of Stitches
Tailoring skill increased by 15. In addition, there is a chance that you will be able to loot extra cloth from enemies.

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The idea is to create a set of racials that will justify any class played as that race, balanced to every other racial/class combination. (That's why I gave Gnomes a boost to both Intellect and Agility. If your class cannot take advantage of one, it can take advantage of the other.)

In addition, a number of "utility" racials add a little fun and convenience specific to that race without impacting PvP or PvE play. This is evidenced in the profession bonuses, Two Forms, Best Deals Anywhere, My Little Gnomie, Reanimate/Cannibalize/Underwater Breathing, etc.

I agree that each race should excel in a particular profession. I think each prof-related racial should come with 1) a number bonus, and 2) a subtle benefit that does not have a direct impact to one's playability in PvP or PvE if a player of that race does not choose to take advantage of that profession. For example:

Enchanting: Chance on disenchanting to receive extra materials.
Engineering: Increased chance of non-combat engineered items working as intended.

As for matching professions to races, the existing racials have already messed up a few of the ties I would have thought more obvious (Herbalism for Night Elves, Leatherworking for Tauren, or giving Undead Alchemy), but here's how I would make it work as they are:

ALLIANCE
Humans – Generic, passive number bonus to all professions.
Dwarves – Blacksmithing
Gnomes – Engineering
Night Elves – Leatherworking
Draenei – Jewelcrafting
Worgen – Skinning

HORDE
Orcs – Mining
Tauren – Herbalism
Trolls – Inscription
Undead – Tailoring
Blood Elves – Enchanting
Goblins – Alchemy

Justification for choices:
I went with Blacksmithing for Dwarves because, except for Tauren and Draenei (which already have profession-related racials), no other race will have access to all Plate and Mail classes. Leatherworking went to Night Elves for similar reasons (as well as flavor), as did Tailoring to Undead.

Of course, there would be one race lacking a profession, so I gave Humans a generic boost for being the definitive generic race. They get no side-bonuses, but they get a smaller boost for any professions they choose (which includes all secondary and both primary professions).