Not exactly mook - the O from Mobile Suit Zeta Gundam is infamous for having enough armor to withstand beam weapons, which go through lighter MS easily.
The Armored Titan from Attack on Titan is described as looking like a normal Titan, only with a heavily armored layer of skin. This allows it to withstand cannon fire and smash open the interior gate of Wall Maria. He's not just a mook though, as besides the power he also has human intelligence and military training.
Star Wars: Destroyer Droids and Super Battle Droids
Extremely common in both versions of Warhammer. In Warhammer Fantasy, probably the most well known are the Warriors of Chaos, who are an army of evil warriors covered from head to toe cool evil armor, though the heavy cavalry for each faction, if they had any, could also be considered this. Even if a faction didn't have that, they would often have some heavily armored foot soldiers, such as the Black Orcs for the Orcs and Goblins. In Warhammer 40,000, all of the Space Marine armies fall under this trope.
Amusingly enough, in the Ork Codex entry describing "Meganobz", massively-armored Ork lieutenants, one of the main weaknesses they have is the fact that because they wear several tons of heavy armor, if they fall over it's nearly impossible for them to get up, and their underlings have to sweat and strain to get them upright again.
Exalted: If you hate and/or hated by the Realm, you start by fighting non-Awakened-Essence Realm enforcers. Survive that, and you'll have to fight the Wyld Hunt (sic), elite Realm squads usually led by a Dragon-blooded and sometimes Sidereals too. Survive that, and you'll eventually fight Dragon-blooded riding Warstriders; though at this point you're usually a One-Man Army and don't have to worry about Realm incursion to your territory.
God of War always replaces the normal undead soldiers with these after a certain point in the game. In Chains of Olympus the Cyclopses also have armored version that you need to break the armour off of before they can be damaged.
Some games in the The Legend of Zelda franchise feature Darknuts and Iron Knuckles, heavily armored enemies that can take a lot of abuse, and in the case of the former, frequently are only vulnerable to sword strikes from behind..
Metroid Prime: The early stages have "Plated" versions of regular enemies who are harder to damage (most are resistant to the beam weapons you have, but not missiles).
Same goes for the Armoured Pirate Troopers in Corruption.
Paper Mario: Koopatrols, which are similar to Koopa Troopas, but with armor plating and a spiked helmet that keeps them from being stomped on under normal circumstances. However, like all other Koopas, their defense drops to zero once they've been knocked down with a jump attack or a tremor.
Modern Warfare 2: Juggernauts. They can take all kinds of damage without even flinching before they go down. Unfortunately under certain circumstances they prove to be fast-charging Lightning Bruisers...
Dragon Ball Z: Buu's Fury, in Babidi's Spacheship, there are Majin Warriors. By that point, you can kill them with a few hits, though some have breakable shields.
Fallout 3: as the PC progresses in levels, the Super Mutants begin to appear decked out in more and more armor. Throughout the series, human adversaries, such as the Enclave troops, tend to have better armor as the player progresses.
Fallout: New Vegas has the NCR Veteran Rangers and Legion Centurions, which frequently appear in the hit squads sent after you when you gain infamy with either faction, in which case they have higher Damage Threshold than their normal versions.
Super Mario RPG: Most of the Mooks Mario Co. fight make reappearances later in armor or armor-like features.
Three Castlevania games feature fleamen wearing chariot-like armor. Take the fleaman's speedy, erratic jumping and combine it with armor and a huge axe capable of doing high damage, and... yeah.
Assassin's Creed has guards wear more armour as they become more proficient, with the most-armoured ones being Elite Mooks effectively identical to full-powered Altaïr in abilities.
Assassin's Creed II has Brutes. All this does, in practice, is give them more health. They're also quite hard to hit with your weapons (as most guards are). Your best bet is disarming them (particularly satisfying in Brotherhood, where you can throw the axe/huge sword right into their torso) and using their weapon against them, or countering with your hidden blade. Which, yes, stabs right through their metal armour on a few particular finishers. Admittedly, some times, Ezio may just be stabbing them through the eyehole. And right into the brain.
Knight-class enemies in Fire Emblem games generally require magic or a very strong axe-wielder to take down. Typically they have lower speed and movement than other classes which makes it easier to surround them and then double attack them.
Promoted units also seem to wear more armor than their first tier counterparts.
In some of the Dynasty Warriors games, the Nanman army wears bamboo armor, which is immune to arrows.
F.E.A.R. games have the Heavy Armor Replicas who usually tot weapons that bring more hurt, typically those that are best used on them instead.
Jedi Outcast has heavily armoured Superpowered Mooks; the Shadow Troopers, who have been given artificially heightened Force powers, and lightsabers, and are protected by (literally speaking light) armour made with cortosis, a metal so tough it resists lightsabers. Good thing it isn't actually impervious to them in this version.
The following game, Jedi Academy, gives us hazard troopers. Their suits are more like Mini Mecha, these ginormous death-suits that let them walk in lava like it's nothing. They're armed with concussion rifles, which will really ruin your day. It's basically the only kind of Imperial that still presents a threat when you've got your lightsaber.
The Army Of Two games have "heavy" soldiers, typically enemy mooks who are wearing some variant of heavy EOD gear who only take damage from behind. In the sequel there are several variants of the heavies, including shotgun heavies (who can count as Lightning Bruiser) while later on there are minigun heavies, grenade launcher heavies, and flamethrower heavies. The shotgun heavies can be killed with concentrated, high-damage fire, especially against the head, while the latter three types can only be killed by shooting specific weakpoints on their backs (ammo canister, grenade boxes, or fuel tanks, respectively).
One level of Syphon Filter 2 has fully-armored mooks who can only be killed with explosives. At least four bosses in the series are also explosion-proof, and must be defeated by unconventional means.
The full-armored mooks return in Omega Strain's International University mission. This time, they can be killed by shooting their backpacks, similar to Girdeux in the first game.
In Iron Brigade, Breakers are slower than the standard cannon-fodder Resistors, but have a thick armored shell that can only be destroyed with explosives (such as an artillery cannon). Once this is destroyed, their mobility increases and they become vulnerable to most weapons.
Borderlands has variants of some enemies, such as Hardened Skags, which have thick carapaces that reduce damage in certain areas. The Lance Troopers also have armour plating over most of their body; Badass Lance enemies are completely immune to attacks that don't hit their unarmoured points.
Borderlands 2 has Armored Psychos in the second playthrough and beyond. Also Juggernauts, even bigger versions of Goliaths with more armor and no weak points. Not to mention Alpha, Elder Alpha, and Fossil Skags, which have tougher and tougher hides; Fossil Skags are effectively bulletproof from the front!
In both games, armor also manifest in changing the damage modifiers to that enemy to be the same as if they were robots (shown with a yellow health bar), which means slightly less damage from regular attacks, considerably less from incendiary, and more from corrosive. The presence of Armored Psychos in True Vault Hunter Mode helps to make up for corrosive weapons doing less damage against shields and flesh enemies than it did in the first playthrough.
Assault types in Battlestar Galactica Online. To illustrate, the weakest of the bog-standard mook Cylon Raiders has 250 hp. The equivalent Assault Strike, the Marauder? 515.
A few times in Max Payne 3, you encounter troops in effectively bulletproof heavy armour who also wield LMGs. Only headshots will take them down. There are two varieties: The first kind needs multiple headshots to gun down, but are thankfully rare, with a cutscene every time one appears. The second only needs one, but is more common and can be knocked down with body shots to make the kill-shot easier.
In Batman: Arkham City, there are mooks that wear armor that make them invincible against Batman's normal Freeflow attacks. To beat them, you must do a specialized Takedown that pummels them relentlessly before delivering the final blow. Normal attacks are the only thing they're immune to however, and anything that works on any other mook still works on them.
They prove more dangerous during predator combat as it's impossible to do a silent take-down on them. All of the ways to take them out produces some level of noise, like the same relentless pummeling as during normal combat which also leaves you exposed for a long time or ledge/inverted take-downs which causes them to scream.
In Mass Effect 3, Cerberus Guardians have a riot shield completely protecting them from weapon and power damage from the front. There are various ways to defeat them: you can shoot them from behind, the shield can be removed using the pull ability, or you can use armor piercing mods or ammo. If you're a good enough shot, you can also headshot them through the eye slot, earning you the "Mail Slot" achievement.
Mooks in Perfect Dark Zero frequently wear either armored vests, helmets, or both. The latter prevents One-Hit Kill headshots with most weapons, although armor-piercing weapons such as the DY-357 magnum can thwart it.
Far Cry 3 has Heavies and Flamers; the heavies wear high-grade bulletproof masks that take entire clips to shoot off, while the flamers have even more armor and are immune to fire. This makes them extremely hard to snipe, but the Heavies don't cover the backs of their heads, and both enemies can be susceptible to a simple Takedown if you select a specific Heavy Takedown skill.
Nintendo Land's Zelda-based attraction has enemies with varying levels of armor. Moblins with pot helmets and metal shields would probably be the best match for this trope.
Sonic Heroes has the Egg Hammers, which have a very high number of HP and can only be defeated by the power character. However, at least this robot is vulnerable all over—there is a Armored variant that wears a helmet and is only vulnerable on its rather small head underneath. When attacking, it is very easy to miss the robot's head completely, even with the Level 3 bomb shower attack, or accidentally run into the robot's hammer once it's knocked over.
Knights and other high end Men At Arms, compared to normal archers and footmen.
There were experiments with issuing body armour to soldiers in World War I, but was considered too heavy and cumbersome to be worth it. Still, a few special units sometimes used it. For example, snipers and machine gun crews sometimes wore it to protect against enemy snipers (the bullets didn't have so much power at long range), tank crews wore it to protect against shrapnel, and German assault troopers occasionally wore it because it was quite useful against pistol bullets and melee weapons.