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, which may have been the basis of their names being recycled in Overwatch.
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.
The Sky Golem and Mechanized Lumber Extractor mounts seem 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.
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 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. One is black. The others are red, green, blue, and yellow. Sadly, they do not combine to form a larger mount.
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.
In Highmountain, the Stonedark drogbar have a snail race, from which you can win a snail named Zoom.
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 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 Stormsong Valley, there are five tameable mechanical tigers called Sabertrons that come in red, yellow, green, copper, and pink. There's also an unpainted non-tameable one named P4-N73R4.
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.