The Magog on Andromeda favored this tactic, most of the time not even bothering with weapons other than their claws and paralytic spit. It was later revealed that these were unknowingly scouts for the real invasion, which had weapons and strategies on par with the other factions as well as numbers.
The Wraith in Stargate Atlantis prefer this kind of tactic. Their tech may have been inferior to the Ancients, but with wave after wave of meat shields at their disposal, it didn't really matter.
The drones in Stargate Universe are somewhat closer to the trope than the Wraith. They use nothing except fighter-sized attack ships controlled by an unarmed command ship, and their sole battle tactic is to attack from every direction until the enemy dies.
This is one of the tactics the The Dominion employs in Star Trek: Deep Space Nine. They have small, 80-120 meter attack vessels that don't have really as much firepower as their larger Federation/Klingon/Romulan counterparts, however, a massive force could be created of them. Case in point, when the Tal Shiar/Obsidian Order attacked the Changeling homeworld with a 'large' fleet of 23 capital ships (Keldon-class Cruisers, Galor-class Destroyers, D'Driniex-class Battleships), the Dominion retaliated with 150 Attack Ships which completely swarmed and overwhelmed the Cardies and the Romulans. They had full-sized warships too, including some bigger than anything in the Alpha Quadrant races' arsenals, but even those could be deployed in massive numbers. The massed Dominion fleet they finally tried to commit when the war was in full swing had more than 2500 ships.
This had The Federation switching tactics as well. During the TNG era, Starfleet was made up mostly of largish general-purpose exploration / diplomatic / science / carrier vessels (with "defensive" armaments equivalent to dedicated warships from other nations) like the Enterprise, supplemented by a few smaller, specialized medical or science vessels. Between the Borg threat and the Dominion war, using general-purpose starships for combat became Cool, but Inefficient, and by the last few seasons of DS9 the Federation was fielding large fleets of dedicated warships and squadrons of starfighters, coming much closer to a Zerg Rush tactic than ever before.
After an initial attack by a relatively small number of Foot Clan ninja in the first episodes of Ninja Turtles: The Next Mutation , The Shredder angrily declared his intention to rally all of his followers in New York City and crush the Turtles with sheer numbers. It likely would have succeeded without the intervention of Venus De Milo, who proceeded to Mind Rape Shredder.
Doctor Who: The Daleks did this in "Destiny of the Daleks," draping some of their own number with bombs and sending them off to blow up the Movellans with predictable results: the Doctor blows them up before they arrive.
Kamen Rider Imperer of Kamen Rider Ryuki (a.k.a. Spear in Kamen Rider Dragon Knight) is contracted to an entire herd of gazelle Mirror Monsters instead of the one monster most Riders have a contract with. His Finishing Move involves the herd running at the foe and hitting him (using looped CG footage), building it up to Imperer himself kneeing the villain for the final blow.
A heroic example in GoGo Sentai Boukenger. After their combined mecha fail to defeat Gaja, they separate all their vehicles and swarm him with all of them at once (combined with a good dose of Heroic Resolve), successfully overwhelming and destroying him.
In The Walking Dead, the Governor admits his people aren't as skilled as Rick's group, but that their numerical advantage makes up for it.
In an episode of Deadliest Warrior, the team ran a pseudo match of Vampires Vs Zombies. It was even admitted that in a single combat scenario, a super human vampire vs 1 zombie would end with the zombie being demolished. This resulted in the team running 3 vampires vs 297 zombies (99 per vampire). The idea of this was demonstrated in the fight, that two of the vampires fell to the attacking zombie forces simply and entirely because they were being overpowered by massive numbers. The last one barely survived the entire battle, as being attacked from all sides for the 3 zombies with what seemed like endless waves of zombies was incredibly difficult.