Death Knight - Blood Elf/Human
I know people have a lot of hate for the male Blood Elves, but lore-wise they make a LOT of sense. Arthas hit Quel'thelas as well as Stratholme and Lorderon hard which would have resulted in high numbers of Death Knights coming from these areas.
Druid - Night Elf
One with the forest and such. Pretty easy one to do. Only reason Tauren aren't on here also is the Night Elves have been druids consistently, and the Tauren only recently started doing it again.
Hunter - Tauren
When I think of Tauren I think about the Native Americans (obviously). These two combine so well that even though I don't play my Hunter as a Tauren, I think it's still the most Lore-Friendly of them.
Mage - Human/Blood Elf
The Kirin-Tor which is pretty much the Mages members only club is mainly comprised of Humans, High Elves and Blood Elves. Since High Elves are an NPC faction for the Alliance though I figure Humans and Blood Elves make the most sense. I mean Quel'thelas is BUILT on a city of magic.
Monk - Pandaren
Paladin - Human
Arthas, Uther Lightbringer/Uther The Lightbringer, Tirion, Bolvar are all some of the greatest (not best) Paladins ever. All human.
Priest - Night Elf (f)
The Priestesses of Elune are the only real reference to a specific deity that comes to mind. And in my mind a priest is supposed to worship something specific.
Rogue - Orc/Undead/Human
This was the hardest one to lock one down on. First off you have the Shattered Hand Orcs, and Garona, one of the first rogues to be introduced to Warcraft way back when (yes i know she's half draenei but they can't be rogues). Then the Undead Deathstalkers. Kind of a stretch but anyone that has a faction dedicated to stealthy arts deserves rogues. Which brings me to Humans. SI:7 and Ravenholdt are two great reasons that Humans get on to this list.
Shaman - Troll
One of the oldest races on Azeroth as conduits for ancient forces of nature.
Warlock - Undead
I just can't help but think that something already undead is something with the least to lose by tapping horrible fel magics.
Warrior - Orc/Human
The name of the first game says it all.