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.
Several jokes, flirts and dances each race has often include shout outs of some sort.
In the Halls of Valor, two of the vrykul kings the group fights before the God-King Skovald encounter are named King Tor and King Bjorn. They were present in the original Utgarde Pinnacle instance during the King Ymiron encounter, so this might be a recursive example.
In Highmountain, there are drogbar mobs called Bitestone Roadhogs. They pull the player toward them with a hook on a chain.
The toy given at Winter's Veil 2016 is Mei's endothermic blaster.
One of the Brawler's Guild solo fights introduced in patch 7.1.5 is a team named Ogrewatch.
One class hall mission is straight-up titled "Overwatch".
Holy paladins can find a skin for the Silver Hand from the "Edicts of the Lost Watcher" item. It turns their hammer into a Magitek version of Reinhardt's.
In Zuldazar, there's a pair of fungarians named Genjo and Hanzin.
A daily quest in Mechagon sends you to kill Junkbrat and Roadtrogg, who are a mechagnome and a trogg wearing a gas mask.
One of the final Highmountain missions, where you ride a giant eagle to bomb Drogbar forces, is called "Justice Rains from Above".
The two characters existed long before Overwatch, but there's something reminiscent about Halford Wyrmbane, Commander of the 7th Legion, and Mathias Shaw, head of SI:7, working together and the former relationship between Overwatch Strike Commander Jack Morrison and Blackwatch Commander Gabriel Reyes. Bonus points for Wyrmbane and Morrison sharing the same voice actor, Fred Tatasciore.
In Shadowlands, male pandaren and female night elves were respectively given hairstyles based on Hanzo and Sombra.
In the fight against the Manastorms in De Other Side, Millificent's line for deploying an Aerial Rocket Chicken Barrage is "Poultry rains from above!".
The vanilla goblin shredder model and the Sky Golem and Mechanized Lumber Extractor mounts have a picture of Sarah Kerrigan on the control panel. Continuing the trend, the control panel of the Mecha-Mogul Mk2 mount has a poster on the right side taken from the box art for Brood War.
Shadow priests have a talent named Legacy of the Void.
A quest in the Legion warlock storyline is called "Power Overwhelming".
In the Horrific Vision of Orgrimmar, the Oblivion Elemental's aggro line is "Oblivion awaits!".
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 the old version of 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 Winterspring, there's a goblin who's named "Umaron Stragarelm", which is a combination of Umaro, Strago, and Relm.
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. Sound familiar?
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 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 ToxicRevenger.
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.
An achievement in the Argus the Unmaker encounter in Antorus, the Burning Throne is titled "Stardust Crusaders".
There's another reference to that in the form of a garrison follower you can recruit named Soulare of Andorhal, a paladin who says things like "Praise the Light!" He even gives you a bonfire with a sword sticking out of it for your toy collection if you use a /tired emote on him.
In regards to Firefly, at Telredor in Zangarmarsh there's a gnome engineer named K. Lee Smallfry. You can give her an engine part you found. In Grizzly Hills there are two women named Saffron and Yolanda, both aliases used by Mal's supposed wife. One of them even has the name Reynolds.
Basically everything related to the Eldritch Abomination Old Gods is a Shout-Out to the works of H. P. Lovecraft. The two gods you fight as bosses even have very similar names (C'thun = Cthulhu, Yogg-Saron = Yog-Sothoth).
When you get to be able to build submarines, one of the possible names is Deep Sea Nine.
One of the Battle Pets trainers uses a floating skull named Mort, a possible reference to Morte, who is also a floating skull.
Getting Exalted with the Order of the Cloud Serpents faction allows players with Jewelcrafting to create five different mounts. Each one is a brightly-colored artificial feline. There are four basic ones- red, green, blue, and yellow. Combined, they form another one -black.
One Draenor quest sends you after a giant named An'dure the Awakened. The quest is "An'dure the Giant".
While Reshad and Percy are rummaging through Syth's scrolls, they find one called "Fifty Layers of Shadow", which Reshad calls erotic sorcery-fiction.
In Legion, part of the questline in Stormheim has you doing quests in Thorim's Peak for a group of dragons. All of the quests you do for them are named after DragonForce songs (For the curious, the ones in question are Wings of Liberty, Heart of a Dragon, Fury of the Storm, Where Dragons Rule, and Cry Thunder!)
Another quest in the Stormheim area sees you having to rebuild a destroyed living statue in order to progress. The quest comes from the statue's head, and you need to find its right arm, right leg, left arm, and left leg. Whether or not the reference is intentional, it feels less like you're restoring a statue, and more like you're trying to summon Exodia the Forbidden One.
Bilgerudder, a giant in Azsuna who uses NPCs as Pokémon, sometimes says "A-B-W. A-Always, B-Be, W-Winning. Always be winning, ALWAYS BE WINNING!
The name of the Shadow Priest's artifact weapon, Xal'atath, sounds very much like Xel'lotath.
Bonus points: Shadow Priests have an insanity theme, and Xel'lotath represents Sanity in Eternal Darkness.
In Bloodthorn Cave on Draenor, there's a pale orc named Gorum. He drops a ring called the Precious Bloodthorn Loop.
In Dalaran is a flower saleswoman named Aerith Primrose. The new version of Dalaran in Legion has her accompanied by a bodyguard named Koraud. He's dressed similarly to Cloud, right down to the BFS.
One of the Hunter Class Hall missions has you investigating the murder of an SI:7 agent. You go to her quarters to find a pair of SI:7 agents already there, two Men in Black named Agent Smith and Agent Jones.
Ysera's death, and her final fate, is quite similar to Draco's at the end of Dragonheart.
The quest for Hunters to recruit Rexxar in Highmountain has you attempting to survive a night in the woods while your vision is obscured by darkness and you must gather meat to fend off hunger, a la Don't Starve.
Speaking of Brennadam, the quest "The Days Are Just Packed" sends you to meet a Seargent Calvin with spiked blonde hair outside the city. Also in town are his pal Hobbs and Babysitter-I mean, Mayor Roz.
A vignette mob in Drustvar's Crimson Forest is a bear named Hyo'gi. He can grant himself a damage buff called "Smarter than Average" and has a self-heal where he pulls out a picnic basket.
After completing the main story for Stormsong Valley, a quest called "Ruin has Come" becomes available. The questline, and the area you go to, are full of references to Darkest Dungeon. Just a few examples include:
The quest giver is named Wayne the Ancestral, referencing The Ancestor's voice actor, Wayne June.
Throughout the quests, a Sanity Meter called "Strain" increases and decreases during your stay. If the meter reaches 100, "your resolve is tested".
Wayne's quotes are randomized, and most of them are direct quotes from The Ancestor.
There are random, out of place spiders and grubs that wander the road, similarly to the random encounters in Darkest Dungeon.
The main area has a few wandering ghostly NPCs that reference the Houndmaster and the Blacksmith.
The Lost Platysaur companion is a reference to Ducky from The Land Before Time. According to the pet journal, it even states that it repeats some short sounds about three times in a row, similar to Ducky's trademark phrase "Yep, yep, yep".
In Hillsbrad Foothills, "The Durnholde Challenge" series of quests ends with you fighting a shapeshifting mercury elemental called the D-1000. One of the items received for turning in the quest after slaying it is the Axe of the Judgment Day.
In Mariner's Row in Boralus, there's a pair of NPCs named Laura Statler and Mark Waldorf who will make a crack about your character as you pass by them.
The northern side of Dazar'alor contains a cave under a waterfall, in which is a treasure chest. The chest contains a small amount of War Resources, but also a grey item called "Weighty Bag of Sand", the hover tooltip for which describes it as "Weighs almost exactly as much as a fist-sized golden statue."
Industrial rock band Stabbing Westward gets a couple of shout outs in Shadowlands:
In Bastion, during the RP dialogue of the quest "Step Back From That Ledge, My Friend," Disciple Nikolon says, "I cannot save them... I cannot even... save... myself..." (referencing "Save Yourself" from Darkest Days)
Maldraxxus features a side quest called "Stabbing Wasteward."
In Ardenweald, there's a transportation network that works through mushrooms called a Mycelial Network.
A Vendor Trash item one can gain from helping Revendreth dailies is a painting depicting three darkhounds baying to the moon, a reference to the 'Three Wolf Moon' image. Another item that can be sold quite casually is a "Miserable Pile of Secrets".
Traveling through the In-Between invokes the feeling of a loadingscreen.
One of the places you can visit for Marasmius's daily quest, 'Into the Unknown', involves traveling to a secret underground Mushroom Kingdom, where you must rescue the Princess Penicilla from Maw-crazed Fungrets, including their ringleader, Bagoom. Marasmius even quips, "Mushroom Kingdom? Never heard of it." And once you fully restore the Mycelial Network, he'll offer a new daily quest called 'Go Beyond!'
In the far end of the House of Plagues in Maldraxxus, there are slime mobs called Turbulent Juices. The tooltip for the spell they attack with reads "Shoots an array of real turbulent juice, it's comin' at ya."
A rare Anima power that drops from the Ghastly Charger (a ghostly horse monster) in Torghast is a beneficial heal-over-time called "Spectral Oats", the preferred treat of a certain phantom steed named Garyl.