Its most touching Shout Out would have to be the Shrine of the Fallen Warrior, located in the Barrens. The shrine is engraved with the initials "MK" and the Spirit Healer that stands over it is named "Koiter" referring to Michael Koiter, a Blizzard employee who died during the creation of the game.
There are, in fact, several such memorials in-game. The closest thing to an Alliance equivalent of the Shrine of the Fallen Warrior is the In Loving Memory memorial. Less seriously, in Outland, there's also a memorial to the cancelled Blizzard game, Starcraft: Ghost.
Another real life shout out is a quest in Mulgore which was made for a kid with cancer (who voiced the quest-giver). Said kid has since passed away.
Similarly, the weapon Merciless Crossbow of the Phoenix has a tooltip that says "Finely crafted to Ephoenix's specification." Ephoenix was the name of Ezra Chatterton's hunter. Ezra had the opportunity to visit Blizzard as part of a Make-A-Wish wish and the crossbow is named after him.
With the introduction of achievements, another slew of references made its way into game, including the possibility to earn the title "Jenkins". Leeroy even got his own card in the TCG.
In Mists of Pandaria, there's an even more direct Gauntlet reference, the quest 'Blue Dwarf Needs Food Badly'. This expansion has more refs per square meter than you could shake a gnomish engineering created Automatic Shaking Stick at, before it blew your hand off.
Ulduar has a boss named Kologarn who has some relatively blatant shout outs. He is a giant construct guarding a bridge (really, he is the bridge) and when first aggroed, yells None shall pass! Being a construct, part of the battle strategy involves destroying his arms. When an arm is destroyed he may yell Just a scratch or Only a flesh wound! among other things.
All non-combat/flavour pets have 42 hitpoints. Apparently, collecting them is the meaning of life.
Cataclysm contains the two main characters from the fanfic Interactive Fiction parody You Awaken in Razor Hill, Tednugent and his pet Scratchfever ('Tednug' and 'Scratchfever' in-game), patrolling the area around the town of Razor Hill. They even perform a little in-joke from the story, highlighting Ted's odd attraction to harpies.
In Dalaran there's a shark in The Underbelly named Segacedi after the Sega CD add-on to the Sega Genesis. He has the title of "Sewer Shark", which is the name of one of the games released for it.
In Outland the Arakkoa capital is called "Skettis". The Arakkoa strongly resemble the Skeksis of The Dark Crystal. Some also make a sort of high, humming sound similar to the Verbal Tic of Dark Crystal's Chancellor.
The first questgiver you encounter upon entering Westfall is a Stormwind chief investigator by the name of Horatio Laine. He wears a suit and has a habit of putting on his shades right as he is making a pun.
In the Pandaren beginning area, there's a couple of ponds with bamboo platforms sticking out of them that turn you into small creatures if you fall in because of the spirits of the animals that died in them were infused with the water. Sounds familiar huh?
The Valley of the Four Winds contains an enemy called a Kernel Sprite.
The ENTIRETY of the Tillers faction, from farming your own crops, to making friends with certain NPCs and giving them gifts, is an obvious shout-out to the Harvest Moon series. Or even Rune Factory, since you can also kill monsters like in that game.
In the Southern Barrens, there's a quest calledDwarf Fortress. It involves helping a goblin steal the plans for a dwarven fortress. Guarding the plans is Haggis Boatmurder. The plans themselves are described as "A depiction of the fortress using primitive icons to represent essential structures."
One of the random phrases that the pandaren afflicted by the Sha of Despair can say is "How could this happen to me? I'm sick of this life.", a shout out to Simple Plan's infamous song "Untitled (How Could This Happen To Me?)".
The announcement trailer for Warlords of Draenor used a dwarf and orc to illustrate the new race models, decking them out in warrior and priest gear, like the two main characters (a dwarf and orc respectively) of the WoW machinima series "Alliance vs. Horde".
In Stormwind's west bank, the bankers on the left half are named Kirsten, Scott, and Thomas (Kristin Scott-Thomas) and the right half are named Olivia, Newton, and John (Olivia Newton-John).
The Sky Golem mount seems to have a picture of Sarah Kerrigan on the control panel.
This is a hold over from every other shredder model with an exposed canopy since the beginning.
The quest "Precious and Fragile Things Need Special Handling" takes its name from the opening lyrics of Depeche Mode's song "Precious".
The achievement for obtaining 150 different companion pets is called "Littlest Pet Shop".
Gorgrond in Warlords of Draenor has a three-headed plant hydra named Biolante.
Gorgrond is also home to a rare botani (humanoid plant creature) named Bashiok. His dialogue consists entirely of the phrase "I am Bashiok", and when you loot him, you can get an item that spawns a dancing treant.
The Viscous Fallout boss in Gnomeregan drops a dagger called the Toxic Revenger.
A pandaren, Zach Chow, has a pet tiger named Azunyan.
A random add in the Tanaan Jungle introduction's Blackrock Foundry, the Blackrock Slaghauler, is simply a shirtless orc hauling molten slag. When you fight him, he aggroes with "Hot stuff, coming through!"
An NPC on the Wandering Isle named Jojo Ironbrow constantly asks you to provide him with hard objects he can test his strength on by smashing them with a single headbutt. In the final quest, you encounter an object that all but gives him a concussion when he attempts to break it with his head. Said object happens to be a solid jade stand.