The Pikmin series contains an inordinately large number of such mooks. For starters, nearly every enemy in the game is going to steamroll over any Pikmin not under your direct control, as a general rule. Secondly, any enemy you can't kill before it notices it's being attacked is going to kill everything attacking it when it realizes it's under fire, as a general rule. Thirdly, such Demonic Spiders are going to be positioned in such a way that either makes it impossible to reach their weak spot or impossible to avoid a direct confrontation, as a general rule.
Literal Demonic Spiders show up in the form of Dweevils, who will steal treasures and run into the midst of the various uber-destructive enemies littering the cave, thus forcing you to either micromanage with a teeny tiny strike force of the appropriate Pikmin or risk your whole party trying to clear some space. The electrical ones are among the most dangerous since electricity is instantly fatal for non-Yellow Pikmin, but the worst one is the Volatile Dweevil. Instead of stealing treasure, it carries a bomb-rock which it will use to suicide-bomb your army.
Orange Bulborbs in Pikmin 2 are somewhat similar to their red counterparts, yet their slumber is much more easily broken. Bulborbs are best destroyed by circling to their back while they're asleep and piling purples or reds on as fast as possible to avoid the dreaded shake (which scatters your Pikmin and let's the thing rampage). Oranges, however, don't let you get close enough to actually DO this, forcing you to either waste a valuable Bitter Spray or sacrificing half your Pikmin to take it down with enough speed to save the other half. Did I mention they also tend to have their backs to the wall and be surrounded by tiny orange sentry Bulborbs?
The balloon-riding Careening Dirigibugs carry around giant bomb-rocks, which they drop in extremely inconvenient places. To kill them, you need to wait for them to drop one in a place where you can avoid it while tossing Pikmin up to the bug itself. The catch? These tend to appear in levels with Bottomless Pits, as well as around enemies who use wind or other methods to scatter your Pikmin all over, making a single unlucky move into a disaster that claims your entire squad and force a reset.
Spotty Bulbears. You know how the aforementioned Orange Bulborbs wake up before you get a proper chance to hurl Pikmin on them? Well not only are Bulbears always awake, but they are always moving on Patrol routes. So if your Mins are carrying an item back to your ship without a guard, prepare to witness a Bulbear dinner. Oh, and if you can sneak up behind it, then you are in for a nasty surprise as they keep their young behind them, who will gladly go to town on your Pikmin while you deal with the adult. It is fortunately only found once in the third game's Story Mode, but it can take quite a few explosions to take it down, not like other Bulborb types.
Gattling Groinks. For one, they have a front guard, so attacking them head-on is an exercise in futility, and you need to constantly flank them. And what's worse is that they attack by launching mortar shots in three cluster bursts, which can take out 10 Mins at the most at a point blank hit, and scattering the rest if they get caught in the splash range. And to top both this and the Spotty Bulbear off, if killed without being shattered, both can regenerate after their death and revive in the second game. So if you didn't take them back into your ship, well.....Have fun.
The Fiery Bulblax, simply because it's the only enemy in the game that absolutely has to be fought by a specific type of Pikmin. Being constantly on fire, only the fireproof Red Pikmin can fight them, since even a petrifying Purple Spray won't extinguish its flames and will still burn all non-reds. They're mostly notable because they're the only enemy in the game where you can't conveniently use the Game Breaker Purple Pikmin, since even Orange Bulborbs and Dweevils of any kind can be stunned to death before they can do anything. In one particularly evil decision of level mapping, one of the harder treasures in the game requires you to kill one of these with only Blue Pikmin by luring it into a pool of water, extinguishing its flames, then killing it before it eats your squad, or worse, getting out of the water and re-igniting itself.
While the Yellow ones are not so bad, the regular white Wollywogs are an absolute pain to deal with, especially when they unexpectedly fall from the ceiling. They are very aggressive and will attack your Pikmin with almost no provocation, leaping ridiculous distances in attempts to flatten them.
Anything capable of inflicting poison or disease in the Warlords Battlecry series. Having your otherwise superpowered hero reduced to 1/8th of his normal health or having the speed and combat ability of a three-legged kitten is especially bad when you're playing as one of the Always Chaotic Evil races who have limited access to healing spells.
Additionally, you have the Minotaur king, a huge minotaur that deals huge damage ignoring armor, has a high health pool, and can inflict fear on lesser units, making those afflicted weaker, slower and sometimes gets them running away from these beasts. Then you have the titans, one of a kind units that have terror, an even stronger form of fear and make the Minotaur kings looks like kittens in regards to sheer damage and HP. Also, they explode on death, killing everything and everyone nearby once they finally go down.
In fact, several factions have their particular Demonic Spider available for production at high tiers, but some stand out far more than others. Case in point, Dark Dwarven Bronze Golems will refuse to die no matter what you throw at them, and their right hook is strong enough to kill just about anything that moves. Dwarven Lords are even tougher, as on top of their upgraded armor (shared with the aforementioned Golem), they can resist half of any elemental damage. They're slow, sure, but once they get to your base, the damage bonus they have against buildings will wreck everything you have better than any siege engine could. Dark Elf Assassins are frail, but they can be massed, and have a small chance every hit to kill anyone, including your hero. Minotaur Kings have already been mentioned above, and also have gnolls with a low-tier assassination ability like the aforementioned Dark Elves. The Empire has elephants, which should only ever be confronted with larger units, as they will stomp the everloving hell out of smaller creatures. Ssrathi can breed T-Rexes, who may be somewhat frail for their size, but have a bite that outdamages almost everything else in the game. Barbarians have Reavers, which are basically an army of Conans with a huge bonus against any large unit on top of huge damage and beefy resistances, making it so that just four of them can take down a titan for one fourth of its cost. Knight Lords are as tough as a golem, their swords are similarly strong, can get upgrades to level up faster, and have a nasty bonus against evil-aligned enemies, so it's quite possible your army of undead and demons will be slaughtered. Flip the alignment, and trade mobility and a little toughness for even more damage, and you get undead Death Knights. Daemons can fly, their whip is a hard-hitter, and have a bonus against good creatures as well, so watch your units if you qualify as such. Archons are basically the Angelic response to Daemons. Orcish giants are skull-bashing, cheaper Minotaur King knockoffs, Elder Treants are some of the deadliest trees you'll ever see, and also split into regular Treants on death, hydras and their stronger elemental variants eat up armies like nothing else, and, to top off this list, the absolute worst of them all are campaign-only, and thrown against you: Floating Skulls. They outrange towers, fire fast, move quickly, hit like trucks, and worst of all, they bypass any and all resistances by way of magic-typed damage. They're somewhat frail once you do actually get to them, but you probably won't. In any case, keep in mind your race, as if you make it far enough, you can rally these guys out yourself (except the Skulls).
Evil Genius features soldier squads who will arrive on your island if your heat rises too high with any of the world alliances. They travel in large groups of four to ten men, and can easily gun down most of your henchmen and minions in seconds, and there's so many of them that even a single skirmish with a single squad of soldiers is often enough to seriously deplete your supply of Mooks—and if you try to use social techniques on them, there's usually so many of them that most of them will withstand exposure to your social minions and continue on their mission to wipe your base out.
On top of that, there's Jet Chan—an A.N.V.I.L. super-agent who can cut through your supply of minions like a hot knife through butter, and can knock out most of your henchmen in seconds. You can't even keep him contained in a holding cell—he regularly breaks out, and when he does he'll usually drop four or five minions at least before they subdue him again. You can't get rid of him permanently until your reach the game's seventh objective, either. And if he arrives on the second island early on, before the base has been partially constructed, you're better off just reloading from your last save.
All the super-agents are like this. John Steele (a James BondExpy), for example, randomly resets the security settings on all your doors and can temporarily sabotage your power generators, disabling most of your base (including leaving all the doors open and traps deactivated). Unlike Chan, you can't ever get rid of Steele until the very end of the game.
Ironically, the easy way to avoid the soldiers starting shooting everyone and everything is to set all the doors to security level 1 (i.e. open to everyone). Soldiers really don't like closed doors and will shoot them. Then, when the doors blow up, the soldiers will go into a shooting frenzy. As long as you don't have any closed doors, trap triggers, turrets, or cameras, the soldiers will not start shooting. In fact, they won't even try to kill your evil genius if they see him, as they're not Assassins. Eventually, they'll just go. The only thing you have to fear is other types of agents screwing up your base in the process.
The first Battalion Wars has Pillboxes. They're supposed to be super strong versions of the MG Bunkers, but it isn't enough that they have explosive shells and side machine guns. No. They have to come with ridiculous health and defense as well. The only reason they go down quickly on a standard run is because in the only two levels where you encounter them, you get Anti-Air Vets, who themselves had too much power and can therefore devastate big targets like nobody's business. Unfortunately, you get the AA Vets in the first place on those two levels because of air units to make your life miserable too. Joy.
Battalion Wars 2 isn't free of Demonic Spiders either. Of course, Fighters, are mostly demonic for a No Casualties Run, but they have their definite responsibility for the difficulty of the 2 hardest single-player missions in the game. Nothing gets really annoying like seeing no enemies nearby and 2 seconds later, one of your air units is destroyed. This forces you to manually control a Fighter, which means if you don't have your ground forces Wait or keep themselves preoccupied (especially irksome to do with the lack of a command like in the first Battalion Wars where it sends troops to a specified location), they will move stupidly (either in circles or into a bad situation) just to try to follow you. Under Siege's second half gives you only air units anyway, but the problem is that you're expected to bomb targets and air units are pretty much Glass Canons now. And just to make this even worse, Fighters can do a barrel roll, which throws off the lock-on of weapons that you need to use to kill the Fighters. None of this would be so bad if your air units would actually try at all to pick up Jerry Cans, though that wouldn't help much with your Fighters occasionally crashing into the enemy Fighters and instantly dying as a result. At least Call Sign Eagle in the original isn't That One Level for anybody who can adjust to the aerial warfare, and that level had plenty of targets for the enemy Fighters and Strato Destroyers. But just for icing on the cake, in The Reckoning, the game's final mission, you don't even get any Fighters yourself to avoid needing to use anti-air units that can get one-shotted by the Battlestation. At least until Pierce provides you with 3 Fighters in his Big Damn Heroes moment—that comes after destroying the 3 Generators they're guarding. And Anti-Air Vets have horrible lock-on range, especially for their job. Argh, argh, argh.
Of course, Strato Destroyers in Battalion Wars 2, having their Elite Mook status discredited as an excuse by the Battlestations, aren't going to be off the hook. Even getting past the borderline Guide Dang It of their weakness in their lack of rear armor plating combined with the fact that they're only in the last part of one freaking level in the entire game—the last one in single player, no less—it doesn't change the fact that they take ridiculous punishment for an air unit, when you already have Fighters, as well as a strict Speed time limit if you're going for rank, to contend with. What is worse is that the Strato can blow most of your forces, including your mission critical Battlestation, to Kingdom Come. It doesn't help that the air units regenerate infinitely and the Battlestation under AI not only targets the lasers defenses (which you can't even lock onto) instead of the Mining Spider itself to get the bloody thing done with sooner to give you more grief if you manually control one of Pierce's Fighters, but also still takes notable damage from heavy laser fire.
Elite War Elephants, the unique unit of the Persians. They're heavily armored, have the highest hitpoints of any land (or sea) unit, just a bit less resistant than an actual building, and they have a powerful splash attack. If you're fighting the Persians, get some monks ready because those are the only really effective countermeasure. Their only disadvantage is being slow, but the Persians have a Unique Research that raises their speed, making them a faster live Rams.
Apart from the Saracen unique units, Mamalukes, which take down elephants, as well as every other cavalry unit (as well as practically every other non ranged unit) with ridiculous ease. Even siege weapons weren't effective, because they were cavalry themselves, and could just charge them down. In online play, these were the real demonic spiders.
Also Huscarls, the Goths' unique unit. They have pretty solid attack, are almost immune to archer fire and they also can be built from barracks, meaning that you'll end up with a near neverending swarm if you fight them. But they have no defense to melee units, so a swarm of Swordsmen or even Cavalry can kill them without problem.
Demolition Ships, ships designed for kamikaze attacks. While they can be quite effective in a player's hands, the AI turns them into a force from hell.
For Halo Wars there's Arbiter, Brute chieftain, Waolverines and Gauss Hogs. Both Arby and the chief can destroy half an army with ease. (The former assumes you have infantry or aircraft.) Engineers can make them as powerful as a scarab with the same number of Healers. Wolverines are inordinately powerful against almost everything but main tanks and counter units.Gauss hogs are DS's for the exact same reason.
The most recent expansion of Europa Universalis III, Divine Wind, has put all of the Horde-type nations as this. Austria also counts if you intend to expand at the expense of the Holy Roman Empire.
Homeworld 2's Vaygr Laser Corvettes. A cheap, yet highly efficient alternative to the faster but frailer Bomber squadrons, a single squadron of Laser Covvettes can tear through frigates and capital ships in fewer hits than two Bomber squadrons can do. The difficulty lies in the fact that frigates and capital ships are a cornerstone of Hiigaran war doctrine, so when that asset's lost, the Hiigarans would've lost a lot of ground. Given that the two best Hiigaran counters to this corvette class (Pulsar Gunship squadrons and Torpedo Frigates) are also easily overwhelmed by their own weaknesses in the Tactical Rock-Paper-Scissors chain, Laser Corvette attack runs become very difficult to deter. Due to Dynamic Difficulty, the Vaygr will have generous amounts of Laser Corvettes in comparsion to the Hiigaran fleet.
The singleplayer-only Progenitor Keeper, a Lightning Bruiser at its finest, is an Attack Dronecarrier whose on-board firepower and armor, surpassing anything short of a Mighty Glacier Battlecruiser, is kept in a package that's smaller and nimbler than a common Destroyer. To make things difficult for the Hiigaran Fleet during the encounter, Battlecruiser technology is still unavailable and the Keeper is scripted to fully recover upon a quick Tactical Withdrawal.
Dawn of War has a few of these: Tau Fire Warriors, which have ridiculous range and stopping power for an infantry unit and is the Tau's basic infantry. Ork Flash Gitz, which have the same resilience as other Orks but with incredible firepower and accuracy, something Orks tend to lack. Chaos Obliterators, Mighty Glaciers effective against all unit types which can teleport. And of course the Necron Lord, which is powerful even for a Commander and becomes a relentless Boss in Mook Clothing with enough upgrades. The necrons also have Pariahs, which have a very powerful melee attack, a decent ranged one, a lot of health, and are immune to morale damage, as well as causing a slight maximum health reduction on enemies they attack but do not destroy. The main thing that stops them from being a Game Breaker is their slow movement and inability to teleport like other necron infantry, the limit of one squad and their cost.
Dawn of War II, meanwhile, has the Zoanthrope, a Glass Cannon that can obliterate vehicles in a few shots, even the Dreadnought in the campaign (otherwise a Game Breaker), and Tyranid Warrior with venom cannon - an annoyingly precise weapon that deals damage on par with the best heavy guns in the game, except that it's fast, doesn't have a minimum range and doesn't need to be deployed.
Eldar Seer Council and Warlocks are even worse, since they can do that AND move incredibly fast and hold their own in melee.
Plants vs. Zombies has the Gargantuars. Sure, they're slow, but they take a crapton of damage (it actually takes twoOne-Hit Kill plants to kill them), One-Hit Kill any plant it comes across, and throws a smaller zombie deep into your defenses when it gets close enough. They also like to attack in groups. And that's saying nothing about the Giga Gargantuars that appear in Survival mode...
In the earlier levels, DancingZombies are deadly because of the multiple backup dancers they spawn. It is very easy for a backup dancer zombie to spawn right behind your plants, and the zombies force you to micromanage.
It doesn't take long to learn to hate Jack-in-the-Box Zombies. They explode at random times and can carve huge chunks out of your defensive lines in seconds.
Ladder Zombies come in and climb over all your defenses, leaving their ladders to let other zombies over. They can be circumvented with Magnet-Shrooms, but the levels which they appear in take place during the day, making Magnet-Shrooms need a Coffee Bean and thus raising the cost to 225 sun plus a flowerpot and requiting two seed slots. The only other ways to remove a ladder are by using an explosive plant to bomb it off (which recharges slowly and is often a waste), by planting a Pumpkin and digging it up, or by digging and replanting your wall (both massive wastes).
The sequel introduces the Gargantuar Prime from the Far Future. Imagine Gargantuar with Eye Beams that sweep your lawn, instantly killing up to two random plants in you back lines. That's Gargantuar Prime for you. These mechs can easily devastate your lawn if not disabled by the E.M.Peach or killed in time.
Mini Robot Wars has the Titan. Like the Giant, it's huge, slow, has a lot of health, and kills your minirobots in one hit. Unlike the Giant, it has about twice as much health and it can kill three minirobots in one blow!
The Mole is this if you don't have anti-stealth units. These are stealthed, and their claw attacks hit an entire column of minirobots, hurts a lot, and hits rapidly. Thankfully, a Radar minirobot or some Surveyor minirobots will lessen the trouble.
BrutalLegend's Campaign mode has one in the ranks of the Drowned Doom army: the Reapers. They move ridiculously fast, can one-shot most of your non-vehicle units with their melee attacks alone, and they have some strange blue fire burst attack that tears you apart in seconds. Oh, and did I mention that there's at least one of them around every time you have to face the Drowned Doom? At least they can be taken down somewhat quickly by Double Teaming with a level 2 Razor Girl...
In fact, ANY Drowned Doom unit is a Demonic Spider, Reapers, Frightwigs and Brides being some of the worst. Reapers (as stated above) can practically murder you and your entire army in about a second, are INCREDIBLY fast, and usually come in pairs of two or three (at least during the later Stage Battles). Oh, and you're screwed if someone decides to Double Team with one... Frightwigs attack using their tentacle-hair, and they can easily butcher you or any unit from immense distances by themselves. If double-teamed with, they can be thrown at enemy-units to possess them, making them fight for you. If it happens to one of your units, you have to take your own unit down. Sounds like fun, right? And oh, the Brides. The Brides are support-units (buffing their own units, and de-buffing enemies) and don't exactly attack, unless someone hits them. If they're hit, the hitter gets a bolt of lightning thrown down upon them, which kills your units absurdly quick if you're not careful.
The Death spell, not a unit itself but when summoned it will instantly kill any unit it can reach by touching it, this includes the monsters of the wizard that summoned it. Still wizards are not targeted by it.
Two of the most dangerous units are Pyro's Warmonger and Charnel's Styx. Both are Glass Cannon that deal great damage; the former has a short range machine gun that rips apart any target in seconds, and the latter has a long range dark lazer beam that can obliderate souls.
In Battlezone there are the Soviet Light Tanks. They come equipped with the TAG Cannon, a weapon that fires a small tracking projectile. If said projectile hits, they'll unleash a huge, almost-impossible-to-dodge wave of missiles. Two good hits can take down basic NSDF tanks and turrets.
Also, the Furies. Their main attack is a bolt of lightning that's hard to dodge, and they have huge missiles with massive damage radii. Worst of all, the regular ones can drop out of the sky on top of you with no warning. The tank versions at least lack the mobility of the regular ones, but they're substantially tougher.
The spider virii in Darwinia can leap over long distances and tear through Darwinians like a laser cannon through butter. Annoyingly, they target Darwinians over player-controlled units, so it's easy to accidentally lead them back to your incubator and watch in horror as the army you've been building up for the last ten minutes is torn apart.
In the original Command & Conquer enemy tanks controlled by the AI would often plow through entire squads of your infantry, the tanks often didn't bother firing but would just crush any troops to death, it was far harder by comparison for the player to pull of a maneuver like this as the AI could move any of it's soldiers at once out of a tanks way, as well as being able to home its tanks in on any stationary infantry.
In the Red Alert 2 expansion Yuri's Revenge, the Allied Robot Tanks are the bane of the Yuri faction's existance. They are faster than the land-bound Grizzly Tank and can cross water with their hover-jets. The worst part, however, is that it is completely immune to the Mind Control units and structures that Yuri loves to use.
The same game has the Libyan special unit, the Demolition Truck. Its special ability is to blow up in a massive nuclear explosion. A fleet of these pointed straight at the enemy base, backed by the invulnerability-granting Iron Curtain, can level a base in seconds.
As the Game Breaker faction, Yuri gets his own spiders too: the Floating Disk is a high level unit that can deactivate your entire base, eat money and are generally a pain in the ass to kill.
The Soviet Terror Drone is this in the early stages of the game. They can't harm buildings, and base defenses tend to kill them quickly. However, they have a one-hit-kill melee attack against infantry. What they do to vehicles is even worse - they jump inside the vehicle, and destroy it from the inside out. Once the vehicle dies, the Terror Drone is free to continue its rampage. The only way to save a vehicle that has become "infested" is to get it to a Service Depot, which the player will often have neglected to build yet. Yuri has it worse - he doesn't get a Service Depot, so all he can do is destroy his own vehicle, which kills the Terror Drone as well. A single Terror Drone can wipe out an entire unit of tanks, or put a serious crimp in your economy by going after your ore miners. The Terror Drone also gets bonus points for looking like a spider.
Since a lot of strategies don't involve air strikes (most aircraft units in the C&C universe are glass cannons at best), a fully promoted Kirov soon becomes one of these. A regular Kirov takes a while to kill thanks to its absurdly high defense. But a fully promoted one takes even longer. If one neglects to build sizable air defenses, by the time a Kirov starts dropping bombs, it's already too late.
Red Alert 3: Uprising's two most threatening units are the Allied Harbinger gunship, which can pulverize anything on land, and have the ability to repair themselves on the fly; and the Empire's Giga-Fortress, that transforms from a slow naval unit to an incredibly durable air unit with a deadly Breath Weapon. Four or more of these are enough to level a base in minutes.
Tiberian Sun introduced the Cyborgs, who are classified as infantry but are uncrushable and have more than average health. They also have a rapid firing weapon that can mow down tanks in addition to infantry. They're obtained rather early on and you can mass them to harass enemies before they can get down a war factory. On top of all that they can heal in tiberium, making them exceedingly hard to get rid of. The Cyborg Commando takes this to another level, being able to destroy anything in the game in 3 hits, including buildings.
Rise of Nations has the Stealth Bombers. Incapable of being targeted by SAM systems, capable of flying at fighter speeds, and inflicting obscenely high damage with laser-guided accuracy, these are the bane of any player, whether online or playing against the computer. The fact that they can't be targeted by SA Ms requires you to spam fighters in order to protect your important sites from them, thus wasting considerable amounts of population. Even worse, they're not really that expensive, meaning that after your enemy has a good infrastructure, he can Zerg Rush you with them, requiring constant raids against hostile airbases to prevent the damn things from destroying your cities and wonders. There's a reason why they've motivated many players to end the game by bringing the Armageddon counter to zero (in Ro N, each time nuclear weapons are used, the counter decreases by one, if it reaches zero, everybody loses).
Company of Heroes: most of the German super units, the Wehrmacht King Tiger, the most powerful tank on the field, and the Panzer Elite Jagdpanther, a power tank destroyer which can penetrate any armoured unit. Both units are Made of Iron and can single handily take on anything in the battlefield, but once destroyed they are lost forever, unless they are repaired by a Bergetiger.
Iron Brigade has the Volt Dropper, boss for the second map and from then on a recurring enemy in regular waves. Circling the battlefield out of range of your mecha, toting a massive amount of HP, only being able to be targeted by a select few turrets and bombing the hell out of your base, this flying nightmare will - unless you spam AA turrets - probably survive into the next wave and still be flapping about whilst you're trying to deal with new enemies, all the time knocking down the health of your installation. When your commander tells you to look up, worry.
Yu-Gi-Oh! The Falsebound Kingdom has Labyrinth Tanks. If they're the leader of a team, they move incredibly fast, and once engaged in combat they hit very hard and are pretty tough to take down. It usually takes a few rounds of combat in order to take down a team with a Labyrinth Tank.
Blood Tricksters. These have quite a bit of health, and will resurrect all slain savages around them into voodoo zombies with a lot of health. Worse still, your towers stupidly attack the zombies instead of aiming for the trickster first! If you don't use a Rain Of Fire or reinforcements to keep it busy, your defences will get overrun by stupid voodoo zombies.
Saurian Savants, if not killed quickly enough. These guys can summon Broodguards (gets faster when near death, easy), Darters (teleports, irritating), as well as Nightscales (cloaks when at half their health, very dangerous). If the Savant summons a Nightscale when it's halfway through, the Nightscale will probably cloak and waltz past half your defences!
The Extra Content chapter "Rising Tides" has three of these:
Blacksurge: This turtle/snail hybrid can temporarily disable all towers in a wide radius around it, and when low on health, it goes into its shell and moves past your troops (When doing this, it's invulnerable, AND it regenerates health very quickly!)
Bluegale: This mind-flayer thing is completely immune to magical attack, and it creates thunderstorms. Which obscure your vision, disables your towers from being upgraded, and deals damage over time in a huge area.
Cursed Treasure has Ninjas. They're very fast, and as soon as they get hit, they use a Smoke Bomb to make themselves invisible for five seconds, meaning they can run past most of your towers unharmed. You'll need to place a mass of towers near your gems so that they get shot in all directions when they de-cloak.
If that wasn't enough, we have Champion Ninjas, who are even faster and have more health * The otherwise-weak Demon Skill tree is your friend here. Max out Meteors and spam them to beat them.
The sequel tones down the ninjas by giving you the Fear spell, which affects cloaked ninjas and pushes them back for a short while. Enter the Iron Guard Champion mooks. Like Ninjas, these robots stealth as soon as they get hit. Unlike Ninjas, Iron Guards are slower, have much more health, AND are immune to Fear, so no pushing them back. Oh, and they can fly over water to take a shortcut to your gems.
The sequel has amazons. When they get down to half health, not only do they lose their armor and move faster, they also disable all towers in a sizable radius for several seconds. A group of these ladies in an early wave is very bad news.