Human Hunter
Nathanos Marris, the first (and only) Human to be trained by the elves as a ranger. If that is not enough, please fly yourselves out to Grizzly Hills, where a fine selection of hunting lodges have been prepared for you. Yes, I know that technically most of these hunters are Worgen now (SPOILER ALERT!), but only after Arugal (SPOILER ALERT!) messed with them.
Orc Mage
All the arcane magic of a warlock without that nasty business about damning your soul. Perhaps the Blood Elves have managed to teach some of the more studious orcs about the secrets of the arcane? Or perhaps, as the WoW comic shows, Garona's orc/draenei/human hybrid monstrosity of a child, Med'an, returns home to show off the fact that he can do everything. Arcane, holy, druidic and shamanistic magic? Kid's a bigger Mary Sue than fucking Rhonin, seriously.
Night Elf Mage
These dudes are the original Highborne. They didn't leave Kalimdor after the Sundering (so didn't become High Elves) and are likely allied with the Shen'dralar in Dire Maul. THIS DOES NOT MEAN THAT THE ENTIRE NIGHT ELF RACE IS PLAYING AROUND WITH MAGIC. Yes, I know that Night Elves hate Arcane magic. Stormwind hates Fel magic in much the same way, but you can still roll a human warlock.
Dwarf Mage
Trivia: Dwarves were actually able to be Mages way back in beta. It was changed close to release - so close that the original manual shows Mage as a possible class option. I know that this doesn't exactly justify Mages, but it's pretty goddamned obvious to be honest. Look at the Dark Irons in Blackrock Depths. Mages (and warlocks). Emperor Thaurissan himself is a mage.
Blood Elf Warrior
While the magic dependancy does make warriors feel a little wrong (which is why they were removed in beta), they can already be rogues and hunters. They aren't exactly mana using classes either. There are plenty of Blood Elf warriors running around in the world, just attack any Blood Elf settlement and they'll swarm all over you. Or try killing Kael'thas Sunstrider and his friends in Tempest Keep - at least two of his advisers are warriors.
Dwarf Shaman
This one is easy - the Wildhammer have been shaman and druids since forever. They're friendly with the Alliance, but prefer to keep to themselves until they're really needed. With the Cataclysm fucking up damn near everything, I guess the Alliance finally called them in.
Undead Hunter
Remember that ranger dude, Nathanos Marris? You may also know him as Nathanos Blightcaller up in the Eastern Plaguelands. Dude even has a couple of plague puppies as pets. But there's an even more obvious one here, one that makes anyone complaining about this particular combination a complete retard: Sylvanas Windrunner.
Tauren Priest
OK, this is where the stretching starts. The first thing you need to understand is that the Holy Light isn't a specific deity or religion itself. Night Elves and Humans follow different faiths, but both can channel the Light as priests. The Tauren belief system is all about the Earth Mother, kind of a personification of the land and nature itself. According to them the Earth Mother has two eyes - An'she the sun and Mu'sha the moon. The parallels between Mu'sha and Elune basically point to them being the same deity, and Elune is where the Night Elves get all their nifty druid spell powers from - things like Moonfire. Now... think about what would happen if the druids tried tapping in to the light of An'she instead. I'll tell you would would happen - a Tauren Priest would happen.
Tauren Paladin
Because if something is worth doing, it's worth doing in plate. Please note in case you are retarded, this does not mean that Tauren will be the same crusaders that humans are. They'll be getting the paladin skill set without all the bullshit baggage that comes with it on the Alliance side, exactly the same as the Blood Knight order. Expect another sweet new IC name for them, something mystical or whatever.
Gnome Priest
Again... kind of a stretch since the gnomes analytical mind doesn't seem to lend itself well to the Light, but they're insatiably curious and must be dying to know how the priests and paladins they've been fighting alongside have been doing those nifty things. Now, after five or six years of hard study, they're getting the hang of it.
BONUS THEORY: Gnomes have always been priests (supported by the gnome medics dressed as priests and casting priest spells inside Gnomeregan), but most were lost in The Incident. With the Cataclysm and the retaking of Gnomeregan (please!), the few priests still around have begun to take on students again.
Troll Druid
Come the fuck on! Trolls have been dealing with nature and the spirits as Shaman since forever and they've been shapeshifting even longer. You want an example? Look at any troll-themed raid in the game. Zul'Aman and Gundrak are probably the best example, especially Zul'Aman since it already features a Bear, Lynx and Eagle (and a Dragonhawk, but whatever), giving a perfect way to introduce those forms IC. Remember the druid quest to talk to the bear spirit at level 10? Now imagine that you're a Troll and the bear spirit is Nalorakk.