In an MMO as big as World of Warcraft, there's plenty of civilization beyond that of the two warring factions. Players meet them when they have to grind rep with races and cultures that live their lives separately from the war and have joined with neither Horde nor Alliance.
There were always fan theories about which new races would be playable, if ever, and if they would be neutral or join one of the opposing factions. Some of the following races are available in the retail version of WoW, although they have to be unlocked first.
7 Furbolgs
This race has been a presence since the earliest days of the MMO. A rite of passage for players grinding past level 50 was making friends with the tribe of Timbermaw Hold so the character could pass through their fortress and get to Winterspring or Moonglade. They're connected to Tyrande Whisperwind and have powerful magical abilities, especially their Shamans. They also have a presence in Grizzly Hills in Northrend and it's one of the most scenic places in the whole game.
The Timbermaw are also the keepers of several precious recipes and trinkets, like the Furlbolg Medicine Pouch and various patterns, and their empire in northern Kalimdor stretches across several zones. There's a closed fortress of theirs in Azshara that looks suspiciously like an unfinished instance, if any of the people thinking about developing Classic+ are listening.
6 Mok'nathal
The Mag'har are another group that would be fun to build, but any Orcs in Outland could be great as a playable race. The Mok'nathal, who are a mix of orcs and ogres, would be interesting for their open hostility to any Draenei but also for their great shortribs, which are part of one of the Outland daily cooking quests.
The Mok'nathal wouldn't be a neutral race but additions to the Horde. In fact, their open aggression to the foreign races they see as invaders, which means demons and Dranei alike, which would be an interesting dynamic for those that played the race.
5 High Elves
The excuse that Blizzard always seems to have for this glaring omission is that there aren't enough of the High Elves to justify adding them to the MMO, and the player probably did kill a lot of them in Warcraft 3 so that seems at least partly legit. However, that went out the window with The Burning Crusade expansion, in which there were at least enough High Elves to become the Blood Elves.
It turns out that tweaking the lore to add another race wasn't such a big deal after all, and players have been waiting for the High Elves to return ever since. There are a few that appear in notable positions in Classic: WoW, such as Sylvanas Windrunner and her sister Vereesa, and there's a whole city in Outland called the Allerian Stronghold that is home to many High Elves.
4 The Dark Iron Dwarves
How many years did players secretly wish there was an innkeeper here so they could set their hearthstone to the Grim Guzzler? Being the residents of Blackrock Mountain and the close allies of Ragnaros, the Dark Iron Dwarves have been a big part of the World of Warcraft ever since the days when the Molten Core raid was the most badass experience in the game.
Blackrock Mountain is big enough to contain a town, Shadowforge City, and no less than five instances: Blackrock Depths, Upper and Lower Blackrock Spire, Molten Core, and Blacking Lair. Dark Iron Dwarves are the enemies of everyone, and they're talented magic users and fighters. These are a playable race on the Alliance side in retail WoW, which makes sense because their new queen is the daughter of Magni Bronzebeard.
3 The Tuskarr
The most well-known faction of Tuskarr in Northrend is the Kalu'ak, and they have the coveted Epic fishing pole that all the coolest players have to get. One of their representatives, Elder Clearwater, appears once a week in Dalaran to officiate the Kalu'ak Fishing Derby.
Players can find Tuskarr settlements all over Northrend, but they are concentrated mostly on the southern coastline and have a handy public transit system available between major towns. A playable Tuskarr race would have bonuses to fishing and other water-related skills, like swimming.
2 Ogres
Every time there's news of another expansion that's going to include a new race, Ogres are considered one of the leading possibilities. They're powerful magic users and intimidating as fighters, and players have known that since they first had to face them, which is early in the game since they seem to live everywhere.
Ogres inhabit the Arathi Highlands, control the vast instance of Dire Maul, and are a strong political force in Outland. Their prowess with magic and obvious advantage in melee combat can't be denied. One of the longest attunement chains in TBC is connected to grinding rep with a specific faction in Blade's Edge Mountains.
1 Arakkoa
The player's first experiences with the Arakkoa aren't exactly positive. There are a lot of sad stories in Outland, and the tale of the Arakkoa Outcasts is one of them. Not all of the Arakkoa are hostile, in fact, there are a few in Shattrath City who are important high-level trainers who see over the only Alchemy Lab in Azeroth that's not in an instance.
One of the most highly intelligent races in Azeroth, the Arakkoa have been compared to Gnomes in terms of their ingenuity. That's obvious by their prowess with magic, but it can also be extended to other skills like Engineering, and considering the complex, elevated structures they build, it's not unlikely.
World of Warcraft is currently available on PC.