Cataclsym did something unprecedented and unrepeated in WoW's history - it gave existing classes to existing races that had not previously been able to play as them. When I first started playing the game, I rolled a human Paladin (the first incarnation of my main, though I did it on the wrong server and only got him to level 7.) When I realized that my college roommate (who had introduced me to the game) was going to be playing mainly Horde, I looked at the Horde races and liked the look of the Tauren. Sadly, no Paladin option for them - in fact, no Paladin option for Horde at all, as this was still during classic WoW. So I rolled a Shaman who is still with me today (kind of my secondary Horde character, though he's sometimes jockeyed with the Undead Rogue for Horde Main status.)
Of course, these days, you can totally roll a Tauren Paladin. (In fact I did - he was the first character I took through the Cataclysm revamp of the old world in the weeks between the revamp and the expansion launch.)
Back before Cataclysm, some races had very limited options. Tauren and Gnomes could each only be one of four classes until Death Knights made it five. You could never see a Gnome healer nor a Tauren wearing cloth armor (well, they could wear it, they just shouldn't have been.)
The expansion of race/class combos was a great thing for the game. One of the big reasons it was so good is that we were finally in a place where you always had an option when choosing a race for each existing class within a faction. In BC and Wrath, Horde players who wanted to be Paladins could only play as Blood Elves, and Alliance players who wanted to be Shamans had to play as Draenei. And from all the way back in vanilla, Alliance Druids were all Night Elves and Horde Druids were all Tauren.
Cataclysm, then, gave us Tauren Paladins, Dwarf Shamans, Troll Druids, and Worgen Druids. Obviously, Worgen Druids were easily implemented given that they were a new playable race, but we got some expansion of the lore of these existing races. Some required more detailed explanations (there was a little scene that Horde players could see in Thunder Bluff in late Wrath where a druid and a warrior discussed how their form of druidism, learned from Night Elves, focused too much on the moon and not enough on the sun - and those two would become the first Tauren Paladin and Priest,) while some were pretty straightforward (Wildhammer Dwarves = Shamanistic society.)
So, could these classes expand further? At this point, it might not be necessary, given that, with the exception of the not-yet-implemented Demon Hunters, every class has some decent options, and every race has multiple options for tanking and healing. But if we were to expand the classes, to which races would they go?
Ok, this can't actually expand, as it's available to everyone. I actually kind of liked that Blood Elves couldn't be Warriors before Cataclysm, as it kind of fit with their snobby attitudes, but oh well.
The only place to go here is Pandaren. There is an NPC Pandaren Death Knight that you can get as a follower from the inn, but the general idea is that the Pandaren weren't really present in Scourge-infested lands. Still, the Wandering Isle Pandaren were supposed to be a bit more cosmopolitan than their mainland distant cousins. Chen certainly got out in the world, so it's actually not that much of a stretch to imagine that some of these guys could have been raised by the Scourge. Still, while you could do it, it's probably not terrible that DKs aren't available for absolutely everyone.
Undead Paladins would either be awesome or infuriating, depending on how hard they work to justify it. Sylvanas has worked hard to turn the Forsaken into an entirely new type of society (one that conveniently reveres her as a god-like figure,) but fundamentally the Forsaken are humans of Lordaeron, and Lordaeron totally had plenty of Paladins. The Light does physically hurt the Forsaken (it can heal them, but it's painful, like cauterizing a wound,) but if anyone would be willing to bear the pain, it'd be Paladins. You could argue that being undead cut them off from the Light the same way that the Broken Draenei were, and I'd totally buy that except that there are definitely Undead Priests (unless you want to argue that they're all canonically Shadow Priests.) Undead Paladins are not something you could brush off - you'd have to work hard to justify it in lore, perhaps as a kind of dissenting faction who aren't so happy about the way that Sylvanas is running things.
I could actually imagine Human Shamans becoming a thing. The reason is that, when in Northrend, we discovered that humanity on Azeroth is descended from the Vrykul. The Vrykul have shamans, and are much more deeply connected to the Titans and the land, so Humans who want to explore their place within the primal forces of Azeroth could maybe work for this class.
The only option left here is Gnomes, but that actually works pretty well. Gnomes are engineers, and they make guns. We see Gnomes wielding guns all the time. Let the Gnomes shoot the guns!
While having hooves is going to make sneaking around tough, we have precedence for Draenei Rogues. The Rangari, while primarily Hunters, also have a number of Rogues in their ranks, and after becoming Broken, Akama definitely took on some distinctly Rogue-like qualities. Plus, Draenei look really cool in stealth.
The options here are just Worgen and Goblins. While it worked pretty well at the moment, it probably wasn't such a good idea to have their starting experience set at a specific time, because it basically makes it very difficult to justify any other classes being made available to them. I'd love to see a Goblin Monk, just aesthetically, but this might be unreasonable to pull off.
Druids have the extra problem of needing more art assets - and I wonder how much more complicated that's going to be with artifact weapons, unless every artifact variation applies to all races. Horde-side, I could see Blood Elves trying to connect with their ancient roots. Yes, they're not descended from the Malfurion-style Night Elves, but presumably the Ancients played a role in their society before the War of the Ancients. Alliance-side, I'd really just like to see Draenei druids because there's a clear animal theme you could use with them - face tentacles and horns! Lastly, I could actually totally get behind Pandaren Druids, as they already worship the Celestials, which are just Pandaria's local Ancients.
This is a bit early, to be fair. As much as I'd love Worgen Demon Hunters (seriously, I've been wanting that for years,) given the backstory they came up with for the playable hero class, the only alternate options I can really think of that are justified are Orcs and Draenei. The Illidari were mostly Elves, but Illidan had the Fel Horde and the Ashtongue Deathsworn working with him. The latter is trickier, as they were all Broken, but you could easily come up with some justification that Illidan found a way to reverse that process using dangerous Fel magic.
Most of the oddly-missing Warlock races were quietly added in Cataclysm, so this one's tough. Draenei Warlocks would be a huge taboo, as, probably, would Night Elf ones (also, it seems like if a Night Elf is going to dabble in Demonic Magic, they're just going to be a Demon Hunter - though you could argue that this justifies Night Elf Warlocks - if they can be Demon Hunters, why not Warlocks?) Finally, the Tauren just don't seem to have any real connection to that style of magic. So, much like Undead Paladins, you'd have to work pretty hard to justify any of these.
Wait, who can't be Mages these days? Tauren? Just Tauren? Ok, Mages don't really need any more races. The Tauren have a much more spiritual way of looking at magic, while Mages are kind of strictly intellectual (or at most, hot-headed emotional.)
Likewise, really just one option here, which are Orcs. The Orcs don't really have any history of Light-based worship or really any of that kind of celestial sense of what is Holy. You could maybe slip in there, using the shadowy side of the Priest to make them all Twilight's Hammer-but-not-insane types. Still, like the other classes available to all but one race, they're probably fine as it is.