The Emperor is often called "Emps", "The Big E", or "The Emprah", as a reference to some characters' pronunciation in Dawn of War.
The Adeptus Custodes often get variations on "Adeptus Bananas" or "Bananamarines" or something along those lines tacked onto them thanks to their tall, conical helmets and golden-yellow coloration.
A popular nickname for the blue-armoured Ultramarines is "Smurfs", which logically leads to their Chapter Master being known as "Papa Smurf". By obvious extension the Ultramarine's Chief Librarian Varro Tigurius is "Brainy Smurf" and the Tyranid character "The Swarm Lord" is sometimes called "Gargamel". Roboute Guilliman is everyone's "Spiritual Liege", including yours. Also often referred to as Rowboat/Rawbutt Girlyman by people who are either annoyed with his frequent in-canon praisedespite being dead, confused about how to pronounce his namenote For those of you wondering, it's pronounced "Rob-oot-ey Gill-ee-man" per the Gathering Storm video on him, or both.
For the Space Wolves, they're typically referred to as the "Corgis", "(Fucking) Furries", "Space Corgis" or some other variation on either dogs or implying they're well, Furries. Applying the word "wolf" to them even more than they already do is also a popular bit of snark amongst both their fans and detractors.
Thanks to Dawn of War: Soulstorm, "METAL BOXES"note METAL BAWKESES? is now a common catch-all term for tanks. 'Spess Mehreens' and 'Emprah' are often spelled and spoken in line with their famously odd pronunciation in the same game.
Sisters of Battle are "Bolter Bitches" or "Nuns with Guns".
Due to their crescent shape, the Necron flyers are often referred to as "Cronssants". Another reason is that during their debut they were rather overpowered, and one of the terms to describe something overpowered in the game is "cheese". One fan even went as far as to mount actual croissants on flying bases to count as Necron flyers.
Failbaddon the Despoiler: Thirteen campaigns in the vicinity of the Eye of Terror, due to poor writing and invoking the number 13, has been interpreted by Fanon as thirteen failed attempts to escape the eye and outright destroy the Imperium. Despite being billed as the worst of their foes, Abaddon's almost every major campaign has ended in failure.note While this might be a deliberately ungenerous interpretation, little information has been given on Abaddon's Black Crusades until recent editions added information for us to know that those campaigns were part of the Long Game to undermine the area around the Eye of Terror and gather superweapons. Once Abaddon got what was needed, he allowed his forces to fracture off to pursue their own goals or fight one another, as Chaos is wont to do. Sometimes known as Failbaddon the Armless, after his tabletop model's reputation for having its arms break off all the time, or "the incompetent fuckwit," for his incompetent fuckwittery.
Shooting phase for the Guard is unofficially called "the laser light show." Similarly, lasguns are called flashlights or laser sights, while flak armour is either cardboard or T-shirts. note A common joke amongst the fans: What do you call a lasgun with a laser-sight? Twin-linked!
On the flip side, they also have the "Eleven Barrels of Hell" Baneblade (which does indeed have eleven gun barrels).
"Space Elves", "Pansy Space Elves" and "Scary Space Elves/Space Drow" are common nicknames for the Craftworld and Dark Eldar, respectively, and are used as often by Eldar players themselves as by players of other races. "Murderous Space Clowns" is often used to refer to the Harlequins.
Ork terminology is also popular, given their rather laconic approach to vocabulary: a melee-oriented army is choppy, a ranged army is shooty (or has lotsa dakka), enemies are referred to as spikeyboyz, panzees, 'umiez, greyskins, etc. Meganobz are refered to as MANz, a fitting acronym of their full name (Mega Armored Nobz), with the popular tactic of stuffing them into a transport and driving it straight into the enemy being nicknamed the "MANz missile".
Several lists have these kinds of names too. Examples include the Flying Circus (any army with a disproportionate amount of flying monstrous creatures) or Screamerstar (a Tzeentchian army based around a lot of Screamers and Heralds of Tzeentch that is basically a flying deathstar unit that no one can put down).
"Super Friends" referred to more obscene and blatant abuse of the allies mechanic in the 6th and 7th edition rules. This only got worse in 8th edition due to the keyword mechanic, which evolved Superfriends into "Imperial Soup", so named because a huge amount of models had the "IMPERIUM" keyword and buffed things with said keyword.
The Primaris Marines have scored a few nicknames since their introduction, including Chadmarines, Nu-Marines, Guillimarines, Primarisues (due to them being presented as superior in almost every way to the original Marines), Primarsholes, and, due to some similarities to Warhammer: Age of Sigmar's Stormcast Eternals, Spacecast Eternals. The latter is actually quite ironic, as Stormcast Eternals were already known as 'Sigmarines', due to the numerous design and lore similarities between them and the original Space Marines.
The Blood Ravens Chapter are often called the Bloody Magpies by fans, due to the enormous amount of relics from other Space Marine Chapters that they have apparently collected over the millennia.
Certain types of units are referred to as "Deathstars", and rose to prominence around 7th edition due to how extremely powerful they were. A death star is typically extremely destructive, is often hard to kill, and usually costs a tonne of points.
Some fans have dubbed the Primaris Chaplain as Reaper due to looking a lot like said character (such as wearing a skull helmet with a hood).
In a livestream promoting the Rise of the Primarch book, one of the Warhammer Community members mentioned the Smurf meme when introducing Roboute Guilliman.
Another livestream acknowledged the meme about the Blood Ravens stealing everything they can get their hands on, along with a disclaimer about the idea being nothing more than fanon.
The Regimental Standard website references the meme of fans referring to Lasguns with a flashlight attachment as "twin-linked". Apparently Guardsmen are known to do this in-universe, and it's punishable by flogging.
When the first preview images for the XV107 were released, rumors began swirling that it was to be a new form of stealth battlesuit. While it proved to be a more normal super-heavy battlesuit, the lore mentioned that its creator had been commissioned to design a new generation of stealthsuit, and shocked everyone when he rolled out this monstrosity instead.
Many fans like to ship Roboute Guilliman and Yvraine, thanks to their stable, mutually beneficial alliance and dedication to ending the millenia old war between their species. Then the Warhammer Community Team bid the fanbase Happy Thanksgiving with this post, featuring the Primarch and the Herald of Ynnead in a loving parody of Rockwell's famous "Freedom From Want" painting.
When announcing the new Squat bounty hunter for Necromunda, GW released a tongue-in-cheek video of Games Workshop employees seeing a request to "bring back the Squats" on Twitter and subsequently heading off to "reset the clock" (an acknowledgement of the old meme that every time someone asks for the Squats to come back, GW resets the timer until it will actually happen). The clock itself is positioned next to two other clocks (labelled "Plastic Sisters of Battle" and "Plastic Thunderhawk" - two other longstanding fan requests that never seem to see the light of day) and when the employees try to reset the clock, one of them accidentally drops it and breaks it. Cue the new Squat miniature from Forge World. Sharp-eyed viewers may notice that the Sisters clock is a few minutes to midnight; Plastic Sisters of battle were announced soon after.
Old Shame: GW regards the Squats and Zoats as "things better left forgotten." However, hints of them do pop up in new material from time to time...
Promoted Fanboy: Matt Ward is an infamous example. Every codex he's touched has had its fluff tortured, turned into a tabletop sweeper or any combination of the three. The only codex that he wrote that isn't universally despised was the Necron codex, and that's because two editors kept him from breaking the game and the fluff. Despite that, the Necrons still had their ancient Egyptian influence heavily Flanderized. The Sisters of Battle codex that he wrote had the opposite of the usual problems: the lore was solid, but the rules (written by Robin Cruddace) gave them significant nerfs.
Screwed by the Lawyers: Games Workshop's legal team is notorious for its zealotry. Anyone making anything even vaguely reminiscent of their models, even fan conversions for the game, can expect to get a cease-and-desist letter in the mail. They also attempted to trademark the name "Space Marine" and their failure to do so led them to change the name of the Imperial Guard to the more-easily-trademarkable "Astra Militarum." They continued this with the release of the Gathering Storm supplements and the 8th edition rules by changing the Eldar race to the Aeldari (as the word 'Eldar' was coined by J. R. R. Tolkien to describe the elves), the Craftworld Eldar to the Asuryani or simply Craftworlders, the Dark Eldar to the Drukhari, and the Tau race to the name of their homeworld, T'au. Interestingly, the Space Marines weren't renamed and are still referred to as such despite this faux pas of patent law (they actually do have a legitimate trademark on the term in the context of wargames, just not on all uses anywhere ever). The existing alternate name "Adeptus Astartes" did suddenly become more prominent, though.
Shrug of God: Games Workshop has deliberately left everything regarding the two "missing" Primarchs open for fan speculation. Other Posthumous Characters, like Commander Puretide or the Silent King, get a similar treatment.
Technology Marches On: While Schizo Tech has a lot to do with it, it's painfully obvious that none of the factions have equivalents to military tech and strategic advances since the 80s when the game was first made, and most the Vietnam War. Even Tau drones are limited to the same kind of ranges as remote-control planes. Artillery especially seems to be at a WW2 level at best.
Urban Legend of Zelda: A common internet theory stated that Games Workshop received/continues to receive royalties from Blizzard Entertainment, as the latter used GW's character designs in WarCraft and StarCraft. A variant claims that StarCraft began life as a Warhammer 40,000 game until Games Workshop pulled the license, leaving Blizzard to turn it into a standalone title. While both parties admit that Warhammer and Warhammer 40,000 did provide artistic inspiration, there was never a formal agreement in place between the two companies. Games Workshop developers were rather pleased that someone had liked their work enough to imitate it, so they opted not to press for royalties (this was back in the days before Games Workshop became known for the aggressiveness of their legal team.)