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.
This was part of the defense of One Piece's 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.
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 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.
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).
Gundam 00 seems to have been plagued by this one because in the series, a lot of Devines and Brings and also the ELS in the movie.
To expound: in the beginning, the only way Earth felt it had any chance of defeating the Gundams of Celestial Being is by overwhelming them with numbers (with varying degrees of success). They were that powerful by comparison. Once everyone has access to GN technology, Celestial Being had to focus better on tactics than just being a few overwhelming powerhouse units to deal with the same mass of forces.
Played straight in the last battle. Ribbons attacks the combined forces of Celestial Being, the A-Law group that defected, Katharon, etc.. with a continuous swarm of Trans-Am-equipped Gaga units. They do little more than activate Trans-Am and kamikaze everything.
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 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.
Used in Baka and Test, 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 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 aliens in both Gunparade 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.
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.
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.
