In practically every Story Arc in Bleach, Hollows are involved in some way, shape or form. In the very first one, they're worked in a Monster of the Week format. In the second arc, they appeared as Elite Mooks in flashbacks, and in the very last act, a group of Giant Mooks showed up to transport the Big Bad to their dimension, Hueco Mundo. Following that, we're introduced to Hollow-Soul Reaper hybrids called Arrancar, who take over the scene as a War Arc erupts between them and the Soul Society. Hell, in the Deicide mini-arc, said Big Bad used the Hogyoku, the same device that created the Arrancar, on himself, but it gradually turned him more Hollow-esque with each transformation. Even in the Lost Agent arc, where the antagonists are essentially superhumans, said superhumans only gained their abilities because Hollows attacked their pregnant mothers in the first place.
The Skruggs of Heroman fill this role from the simple fact that they NEVER. EVER. Seem to stay beaten.
The Beastmen are this for the first half of Tengen Toppa Gurren Lagann. After suppressing the humans underground for who knows how long they had it a long time coming too.
Nazis in Hellboy. Of both the Steampunk and magical varieties. While the larger threat is always from Eldritch Abominations, the various Nazi factions have a bizarre habit of being involved with almost every story arc in one way or another, even if the arc had nothing to do with them. One chapter hung a lampshade on it when Roger and Abe find (an utterly inexplicable and with no plausible or possible reason for even being there) a Nazi submarine in the ancient tunnels of a lost civilization beneath the Himalayas. They aren't remotely surprised; the damn Nazis have shown up everywhere else.
The "stupid stupid rat creatures" from Jeff Smith's Bone.
In The Hitchhiker's Guide to the Galaxy, Arthur and Ford haven't seen the last of the bloody Vogons after getting thrown out of an airlock by them. Vogons don't like leaving jobs unfinished.
The original orcs of the Lord of the Rings and The Silmarillion are distressingly numerous and fertile, and they will not stop attacking humans, elves, and dwarves even when they aren't enslaved by the current Dark Lord.
Green Martians in general in John Carter of Mars (with the exception of the Thark horde, who are allies of the heroes from the end of the first book on). Not really Always Chaotic Evil (they're a brutal but honorable bunch), but with a culture where you win honor through successful raiding they'll jump at the chance to attack anyone passing through or near their territory, making them a perennial headache for any Barsoomian hero.
The various Shadowspawn in The Wheel of Time, but predominantly the Trollocs and Myrdraal. They do appear to be a serious challenge in massive forces, but seem to be little more than an annoyance for several of the major characters, especially The Chosen One, late in the series. In fact, the use of them can be seen as akin to a Zerg Rush.
Extremist Muslims in the Paladin Of Shadows books, although the subtype varies; terrorists, Chechen paramilitaries and slavers have all shown up.
Live Action TV
The Peacekeepers from Farscape fulfill this rather nicely. They hunt down the main protagonist for two seasons under one crazy commander after another for what amounts to being in the wrong place at the wrong time. And then things get worse.
There's hardly a person in Andromeda who doesn't hate and fear the Magog. Being the followers of the living embodiment of a dead galaxy, those reactions are well earned.
In Babylon 5, the Raiders fulfill this for a while, until they are promptly defeated for good about halfway through the first season. Afterwards, it uses different adversaries.
The Romulans were closest to this trope in the series overall; the Borg made relatively few appearances, the Klingons weren't enemies anymore (though individual Klingons often were), the Ferengi were quickly pushed aside, and the Cardassians only showed up towards the end of the series.
Despite the quote at the top from The Simpsons, in the original Star Trek the Klingons made only about three or four appearances in total. In Star Trek: Deep Space Nine there was even an episode where all three of the lead Klingon villains from each episode showed up, which demonstrates how rare they were. They are more common in the movies, but even then, it was usually rogue elements rather than The Empire itself.
On the other hand, as the show went on, every third episode had a Recycled Script, so while the bad guys in a given story were technically different, they tended to be extremely similar to villains from before and had almost identical schemes; the usual type of adversaries were very common.
Actually, the Klingons had seven appearances in the three season original series. They were introduced late in the first season, then appeared three times in each of the next two. The reason they became the main recurring villains instead of the Romulans was the show's tight budget. Their make-up was easier, cheaper, and less time consuming than the Romulans. Kor, Koloth, and Kang were the main ones named. Usually, the Klingons went unnamed, just showing up at some point in an episode to cause trouble. Hence, the Simpsons parody.
Any faction in Warhammer 40000 would count, though a few stand out because they're easy to write as a faceless, looming threat:
Orks, specifically because they reproduce by dying, and are the most numerous species in the galaxy.
Chaos Cultists, because they're the most numerous faction of the biggest evil in the galaxy.
In the default setting for Dungeons & Dragons, undead are often portrayed as the most hated creature type in the setting, even above fiends. Sometimes, even Neutral deities will encourage their followers to wipe out any undead they find. A quote from a cleric states that he fights dragons because he wants to. He fights undead because he has to.
Tolkeen was a peaceful, accepting, integrated kingdom in a mainly magic-based society. The Coalition States went to war with them, forcing them to leap off the Moral Event Horizon in an effort to survive. It ultimately failed. This is not the first time the Coalition has done this. Similarly, Free Quebec was actually a member of the Coalition, but felt they were getting sidelined, and quite possibly lied to, by the Coalition's leaders. All their suspicious were absolutely true, resulting in a costly war between what should have been natural allies. Even for those who think the Coalition might be right, they're hard to love.
At the same time, Chi-Town (founder and seat of power for the Coalition) was pretty tolerant and open until Nostrous Dunscon decided to declare war on them and fling hellish magical Nightmare Fuel at them. Kinda hard to blame them for thinking magic was evil after that.
In Werewolf The Apocalypse the Garou player characters often have to fight neverending hordes of banes (especially scrags), along with the heaps of fomori and Black Spiral Dancers.
In Exalted, some player character splats can be each others' Usual Adversaries. Notable are the Dragon-Blooded Dynasts and their Wyld Hunt, constantly trying to kill the Solar Exalted and their reincarnations over and over.
While it can be applied to Beastmen as a whole, it's generally Quadav, Orcs, and Yagudo for Bastok, San d'Oria, and Windurst respectively.
Meanwhile, Aht Urhgan is almost constantly Besieged by Mamool Ja, Trolls, Lamiae and their Undead Mooks. Yeah, those folks have a real talent for PR.
Tsukihime: Vampires. Except Arcueid. Mainly because all the vampires shown except Arc are completely fucking insane and very deadly. Arc, on the other hand, is a cheerful, huggableCloudcuckoolander. Unless you're Ciel or have any connection with her at all.
The Noxians inside League of Legends have a general belief in Chaotic Evil and success by whatever means necessary, causing them to support and aid many clearly bad people to become champions inside the universe, or harm many others which then pisses them off enough to become champions also.
The Mass Effect series has the Husks, especially in the first two games.
In the backstory, the rachni and the krogan individually threatened the galaxy for centuries.
Mass Effect 1 had the Geth popping up everywhere, threatening civilization as we know it, though several krogan clans work with them.
In Mass Effect 2, the main enemies are various N.G.O. Superpower mercenary groups, like the Blue Suns. Unlike the Collectors, the true antagonists of the game, the mercs are never really acknowledged to be that big of a threat by anyone, but they're everywhere, and usually stand in the way of whatever Shepard's team wants, especially when it comes to the loyalty missions.
And in Mass Effect 3? Cerberus themselves become this. The Reapers are the Big Bad, and the various forms of husks are their main mooks, but Cerberus just hounds Shepard's team everywhere they go, from Mars to the salarian homeworld, trying to screw up whatever Shepard's team was trying to accomplish.
Halo has the Covenant as enemies in every single game. The Flood appear in Master Chief's storyline a lot, but are not in Reach and ODST, and are absent in Halo 4 with the exception of Infinity holodeck simulations of ex-SPARTAN combat forms.
Cyborgs in The Dishwasher. By the time of the game, about the only people that like them are themselves and the people (trying) to use them. About the only sympathetic cyborg we see is Yuki, the Dishwasher's stepsister. And even then, only for a time.
Touhou has the Fairies. They seem to have no aim in life other than to wear you down before you face the boss of the current stage. They are nowhere near the nastiness of other examples in this page, it's just the thing fairies do. Oh, and don't feel bad about shooting them down, they are effectively immortal.
Just about every canon campaign in Battle for Wesnoth has the player fighting either Orcs or the undead. Even the one in which the protagonist is a necromancer.
The varied and sundry species of Windbag in Bastion, which are all technically different stages in the lifecycle of the same lifeform. They used to live underground and not bother humanity much, but now there's no underground left and they're vaguely aware it's humanity's fault, so they're sort of pissed. Also, humans kind of use Windbag nurseries as power sources, which they're probably not thrilled about either.
In Fallout New Vegas, the Fiends serve as this to the NCR troops of Camp McCarran and to the Mojave as a whole. The player can accept bounties on their leaders that will end up weakening them and lead to their defeat in the epilogue.
For the Fallout series as a whole, the Khans serve this purpose, having been enemies of the NCR since the very beginning and continually surviving despite being nearly purged by both the Vault Dweller and the Chosen One (though the Courier can potentially finish the job). Other contenders are Super Mutants, and the Enclave.
Strega of Persona 3, a Terrible Trio of Persona users who antagonizes the heroes throughout the game. However, aside from killing Shinjiro, they are more a nuisance than anything and usually don't put up much of a fight, though in their defense you'll always outnumber them and you never fight them altogether.
In Starcraft II, the Tal'darim fill this role. In some missions, the Taldarim make over the top threats ("We will pursue you to the end of the universe, James Raynor!"), to which Raynor reacts with merely annoyance. Raynor spends most missions fighting the Zerg, or the Terran Dominion.
The Diablo series, as one can probably guess, primarily has the demons of the Burning Hells in this role, though undead are also a big threat early on.
The Dark Coven led by Maghda causes a lot of your problems early on in Diablo III before the demons proper take over the role for the rest of the game.
First, trolls. They have different subspecies present in every continent, all of which have a instance dedicated to destroy their empire. Every expansion has added new trolls to kill, to the point that players are now expecting a troll raid dungeon for every new content. Not too bad at first, it becomes especially noticeable in Burning Crusade, where the story stops being about fighting demons and other new ennemies in an alien world to be about fighting the same old trolls back home, and in Cataclysm, where the players have to stop fighting a global war against the other faction as well as a world-endangering alliance of several independant factions working for the Old Gods to defeat two troll empires that they have already defeated in the past.
Then, ogres. They don't have as many instances dedicated to kill them as trolls, but they make up for it by being everywhere, including in places where they couldn't possibly be (Gilneas and Kalimdor). They're also in practically every mercenary and criminal organisations. Pretty good for a species that's not even from this world.
EverQuest is set up so that most individual cities have Usual Adversaries. Freeport has the Deathfist orcs, Qeynos and Halas have the Blackburrow gnolls, Kaladim has the kragplooms, Felwithe and Kelethin have the Crushbone orcs, Oggok has the Tae Ew lizardmen, Grobb has the frogloks of Guk, and Erudin and Ak'Anon have wild kobolds.
The Dawn Of War series and Warhammer 40000 Space Marine have Space Marines, Orks, Chaos Space Marines, and Eldar duking it out on every world from here to Eye of Terror and back. Occasionally some combination of Tau, Imperial Guard, Necrons, Tyranids, Dark Eldar, and Sisters of Battle join the fray. Because of the Grimdark, most or all of them are working against each other at any and all times.