A large horde of Titans rush to the Female Titan and eat their target before they can be stopped, allowing its pilot a chance to escape from an ambush.
Also how the Rogue Titan falls after its rampage in Trost (but not before murdering all the titans in said rush) and how Erwin tries to deal with the Armoured and Colossal Titan kidnapping Eren.
Pretty much the only tactic that normal Titans have, which is also what makes Abnormals and the Shifters so dangerous.
Thanks to his new found power as the coordinate Eren is able to use normal titans in this way, siccing huge horde on Reiner and Bertolt
Used in Baka and Test: Summon the Beasts, Class F sets up traps so that they can overwhelm Class A students one at a time. Pretty effective until the rest of Class A breaks down the desk barrier Akihisa set up. In another summoner battle, Akihisa tricks the FFF cult to sacrifice themselves by declaring their enemy has a girlfriend. It works well enough to let him slip by.
The Safeguard in Blame!!, since they have many a Mook Maker on hand and act as little more than a kind of elaborate anti-virus system (if the virus was humans).
In D.Gray-Man the Millennium Earl launched a siege on the Exorcist's base to retrieve a bit of Applied Phlebotinum from them. It consisted of vast numbers of Akuma, which most Exorcists are capable of dispatching with relative ease. It nearly worked too.
A non-violent version appears at the climax of Durarara!!'s first season, when Mikado Ryuugamine publically confronts Namie Yagiri in a crowded hotspot of Tokyo nightlife: admitting he has neither "the power nor the wisdom" to reason through her delusion, he will instead rely on numbers, and presses the "Send" button on his cell phone. Every phone for at least a city block goes off at once with an incoming text, simultaneously revealing every single person present to be a member of the Dollars, and Mikado himself to be their mysterious, urban-legendary founder, intimidating Namie and her mere handful of armed goons into retreating. Well, okay, Celty driving down the side of a building and going berserk may have helped that along a bit, but still.
The aliens in both Gunparade March anime series follow this trope only by virtue of their superior numbers and mindlessness. Individual units are stronger than even the Humongous Mecha of Earth (let alone more conventional vehicles, which are present in greater numbers) and the latter are forced to survive via better tactics and superweapons. Orchestra does show humans finally catching up with genetically engineered Mons.
In Hellsing Alucard's level 0 releases the sum of all the millions of souls he's collected over the centuries, literally drowning entire armies in them. The irony is that a variation of this trope is The Major's tactic against Alucard. First he let's the vampire battalion murder most of London resulting in above 3 million deaths. Then the Vatican's army arrive and fight the vampire battalion. Alucard shows up and uses his level 0 state to kill them all. The goal is not to hope that his large army will kill off Alucard but to trick him into believing that this was their plan causing Alucard to believe he had been victorious. This would cause him to start to absorb all of the blood (and with it the souls) of all the millions that have died. Then Schrödinger would kill himself and be absorbed so that Alucard would gain his reality warping powers which would cause Alucard to cease to exist.
In InuYasha, Naraku's minor yokai do this almost every time, with nearly identical results.
Lupin The 3rd: The Board Game starts the game with at least 8 cops to support Zenigata, so that player can try to Zerg Rush Lupin and the others. It probably won't work any better than it usually does, though.
Lupin III anime episodes and movies sometimes have hundreds of police officers with Inspector Zenigata on the "Lupin Taskforce" to capture Lupin by sheer numbers. Green vs. Red reversed it by having a rush of hundreds of Lupins at one point. It Makes Sense in Context.
In Mazinger Z, often Baron Ashura sent large numbers or Iron Masks to attempt to murder Kouji Kabuto -and his friends- when he was out of Mazinger-Z or to try to overwhelm or get Mazinger-Z and Aphrodite-A confused (and it worked with Aphrodite once. They were so many, so fast and so annoying they got her distracted and slowed her down). Curiously, it was inverted in the original manga once: in one of the first chapters three Iron Masks crawled in Kouji and Shiro's home and they almost got Kouji killed.
In the original manga Dr. Hell also used that tactic in the Final Battle, mobilizing two of his armies, a Cool Ship, a Cool Airship and forty Mechanical Beasts against Japan and the Mazinger army. In Mazinkaiser Dr. Hell also used twice that tactic (and it worked in one of them!) and The Mykene Empire sent huge numbers of Warbeasts all over the world to conquer the surface. Similarly, the Vegans from UFO Robo Grendizer attacked Earth cities with vast fleets of mini-ufos, often backed by at least one mothership and several Saucer Beasts.
In the first season, the three superpowers believe the only way they stand a chance against the technological superiority of the Gundams is to dog-pile them with as many mobile suits as possible (with varying degrees of success). Once the playing field is leveled by a mysterious benefactor handing the militaries their own GN Drive-powered mecha, the Gundams had to start fighting smart just to survive.
In the final battle of the second season, Big Bad Ribbons Almark's master plan involves cheap mass-produced mobile suits, piloted by clones, which use Trans-Am to become almost unstoppable kamikaze missiles.
In the movie, the ELS mostly rely on this because in their first few encounters with humanity, they don't have ranged weapons. Of course, they also assimilate both organic and inorganic matter on contact, so they probably would have resorted to ramming speed anyway. One character in the final battle bemoans that the human forces are outnumbered over 10,000 to one... and it's not clear whether this is intended to be hyperbole.
When he begins to seriously utilize them for scouting is after he realizes that any knowledge the clones gain is assimilated back into himself when he dismisses them. Along with his unusually-high chakra this allows him to summon entire fields of himself to all train at the same time - enabling him to do so hundreds if not thousands of times faster than a regular person and thus allowing him to perfect ninjutsu that normally takes 20 years to master in less than a week.
And don't forget Madara's one hundred thousand Zetsu plant-men army made with First Hokage's chakra
The samurai of the Land of Iron charge Sasuke when he threatens the meeting of the Five Kage. Of course, Sasuke has finally become so enraged with everything that's happened, that he hacks his way through a good half dozen of these men. In hindsight, he gave them a chance to back off.
This was part of the defense of Enies Lobby. A 10,000 man force of Mook Marines and other forces set to defend against any attempt to attack against it. While Luffy single handedly defeated a good tenth of that force and more fell to the allies the Straw Hats brought with them, the power of the Zerg Rush kicked in after the Straw Hats got to where their battles with CP9 would take place and their allies were subdued and captured.
Don Krieg and his pirate armada presumably utilized this tactic as well. While they call themselves the strongest pirates in the East Blue, Luffy informs them that they're just the one with the most people.
Fifty ships. 5000 men. East Blue calls it an invasion force. The Grand Line (Mihawk in particular) calls it target practice.
This tactic is pretty much useless now against the protagonist and in the majority of the New World. The ability "Conquerer's Haki" allows the user to impose their will on someone, and, if the target's will is weak enough, knock them out. Luffy used this ability to knock out 50,000Mooks in one blast - and the only reason he didn't knock out the other 50,000 is because his crew needed someone to fight.
The climax of Pokémon: Destiny Deoxys has the security system of LaRousse City going haywire after Rayquaza's rampage on the city. The security robots go and attack Rayquaza (as well as the two Deoxys when they attempt to protect Rayquaza) en masse until Ash shuts down the system.
In Pokémon Special, a whole bunch of Unown that the Sinnoh trio saved in a previous occasion bombard the Galactic grunts blocking the entrance to the Veilstone Galactic Building so that Pearl can sneak in unnoticed.
The main tactic of the Invid in Robotech is to overwhelm the enemy with enormous numbers of technologically inferior mechas. Best seen in their assault on Tirol in the Sentinels movie (in which the defences of Tirol's capital exact a heavy toll on the attacking Invid scouts and a squadron of bioroid apparently manages to stalemate them... And then three Invid carriers show up and unleash six hundreds shock troopers. That's just the vanguard, the first wave is still arriving. Note that here the Invid are at their weakest and less numerous) and the Battle of Reflex Point at the end of the series and Robotech: The Shadow Chronicles (in which the Robotech Expeditionary Force shows up with a large fleet, opens fire on the Invid carriers to inflict as much losses before they can launch... And the Invid still come in such numbers they grind down the REF fighter complement and manage to ram their motherships. This is with a ground assault on their main installation tying up much of their forces).
Seen in Sword Art Online, when the Aincrad Liberation Front (also known as just the Army) rushes a floor boss with precisely zero preparation. They didn't even scout first. The ones who rescued them are more than a little pissed at their stupidity, and explicitly call them a "zerg-rush guild." It later turns out that there is a political fissure in the guild, and the leader of one faction managed to trick members of the other into using this tactic.
The Gunmen of Tengen Toppa Gurren Lagann appear in massive numbers when engaging in large scale combat, at the command of their respective leaders. To a much more frightful degree, the attacking forces of the Anti-Spiral race work in deadly efficiency. Fresh troops come in increasingly greater numbers as fast as they fall, pulling out the wrath of lethal bait-and-switch tactics designed to kill an enemy the moment the underestimate their foe.
Hakumen, the Big Bad of Ushio and Tora has the Hiyo, small yokai minions spawned from Hakumen that looks like a flying eyeball with ears. They can combine together to form a stronger entity or attack en masse in huge numbers. They are also capable of eating specific memories in humans and monsters alike.
In Valvrave the Liberator the Dorssian forces often launch these kinds of attacks-its less because numbers are all they have, and more because the heroes have a very small force. The Valvraves can stop most of these, but often they need superior tactics, provided by LElf to win, and sometimes they just have to run away.
On both Lion Voltron and the original GoLion, the Red Berets were a small but terrifying force, whether in the very bloody original or the bowlderized adaptation. In both instances, either through murder or just creating terror and chaos, they had the population shuddering inside the Castle, demanding angrily that their heroes protect them and on the edge of despair if not revolt. But when the Berets show up even there, they swarm Black Lion and explode, their dust covering the lead Lion with gunk that renders it immobile and therefore unable to join the others when the giant enemy monster shows up. This all may have been a sign of the growing desperation of the evil lead trio, in that they didn't think this through. The Berets were causing a lot more damage and terror than many of the enemy attacks, but were traded for disabling one of the Lions, which by that late point in the series, the heroes had gotten very good at undoing.