Mushishi, while Ginko is normally a Friend to All Living Things and incredibly forgiving to even the most violent or dangerous mushi, his response when confronted with a species of Mushi that exists solely by preying on people is to explain calmly that humans and that breed of mushi cannot coexist, and humans are stronger.
In Gunbuster, the space monsters are described as a galactic "immune system" trying to wipe out the "disease" of humanity. Humanity is aware that their winning may carry consequences for the galaxy, but decides "Fuck that, we're gonna try to survive anyway."
Mobile Suit Gundam SEED: The war devolved into this after the destruction of the Eurasian military forces at JOSH-A, the Earth Alliance was quick to adopt extremely dubious policies like using drugged up Super Soldiers to keep up with Zaft's genetically enhanced ones, and ZAFT used Genesis to microwave their enemies alive.
The Veigans and Earth Federation Forces also apply in Gundam AGE, all of the Veigans are fanatically loyal to Elzecant and the Earth Federation knows nothing short of the extermination of the Veigan will stop them.
This is not the case in Superior, but most side characters think it is, as does the female lead. The primary conflict between her and the male lead is over whether a peaceful solution is possible. (To make matters worse, they're supposed to be leading opposite sides of the fight—she argues with herself quite a bit over why she hasn't just killed him if she's so certain he'll have to die eventually.)
Then it's revealed that the Hideauze are genetically altered Humans. Suddenly, Ledo begins feeling a lot of guilt.
The primary conflict between humanity and the Titans in Attack on Titan. Humanity is on the brink of extinction, and the protagonist's stated goal is to wipe the Titans from the face of the earth so humanity can be free again. Then it becomes complicated, zigzagging all over the place. At least some of the Titans are actually humans with a Lovecraftian Superpower, utilizing a trio of Tyke Bombs to carry out the extermination. All three begin to crumble under the guilt of their actions, revealing the enemy isn't as mindlessly evil as it seemed. Then the protagonists learn that all Titans are human, merely innocent victims merged with a monster and unable to control their actions. The senior members of the Survey Corps are deeply shaken by this revelation.
Witch Hunter has a Guilt-Free Extermination War on both sides of the conflict. The human side began to kill witches as a new and powerful religion that spoke against them began to spread, leading to the death of countless mostly innocent witches. In answer to this, the witches began their own war against the humans, wiping out whole countries using their magic and powerful familiars. The humans in answer to this, started an Organization called WH, made up of powerful humans and witches, with the stated goal of capturing and restraining as many witches as they can, locking them up and draining them of their powers. The main problem is that many of their more power non-witch members despise witches for their actions and kill as many of them as they can, well also wishing to kill the ones that fight for their side.
Metabarons Universe humanity is threatened by an alien invasion. Rather than waste resources fighting a war, they agree to a battle between two champions. The loser commits "immediate racial suicide." This is perfectly in keeping with the Metabarons storyline, where everything is cranked Up to Eleven.
Independence Day: the aliens, in keeping with their Horde of Alien Locusts, have no issues wiping out entire cities full of people. Humanity has no issues returning the favor for the alien mother ship.
The US President actually does probe for peace even after they destroy every major city on Earth, with an alien that had just slaughtered a team of scientists no less; the response was a Mind Rape that would have killed him if the alien wasn't shot, and it showed him that their entire civilization is based upon this, moving from one world to another, wiping out the natives, using up all the resources, and then moving on to the next planet to repeat.
In Pacific Rim, the Kaiju are here to kill humanity. There's nothing to hold humanity back from punching them in the face in turn, and eventually sending a nuclear warhead back through the interdimensional gateway to hit the Kaijus' creators.
The Martians in Mars Attacks!, they invade Earth and massacre everyone with glee. Then the humans in turn do the same to the invaders when they figured out their weakness.
In Thor: The Dark World, both the Asgardians and Dark Elves are okay with exterminating each other to the last. This is explained because the Dark Elves, created before light itself existed, can only really survive in the dark. Since every other race needs light to survive, it makes it an Us Or Them war for both sides. Even Odin and the new, conscientious Thor never really pause and say "There must be a peaceful way...right?"
Pandora's Star includes an implacable hive mind whose only motivation is to be, not just the only sentient being in the universe, but the only life form at all, and has no problem wiping out humanity. Given that its entire species consists of a single individual, victory for humanity would by definition leave it extinct.
Lensman stories by E.E. "Doc" Smith: The conflict between Civilization and Boskone was a fight to the death. Neither the Galactic Patrol nor the pirates of Boskone ever surrendered to the other, and entire planets were destroyed in the conflict. The justification was that the Eddorians (the beings behind Boskone) are completely amoral and implacable beings from another dimension who consider plundering whole universes to be not just acceptable but de rigeur (they did just that with the last dimension they inhabited), and their hierarchy was based upon that philosophy.
It's actually more complex than that. The major effort and significant part of the plot is dedicated to capturing "brain" Bugs, in order to understand their psychology and see if it is possible to reach an understanding. It's after succeeding in this task humans conclude that the only way to end war is to wipe Bugs from the face of the universe.
Old Man's War by John Scalzi initially presents humanity in a constant state of war with other species for colonies, using a similar justification to that of Starship Troopers (one of Scalzi's inspirations) in that "this galaxy ain't big enough for the two of us". But it is subverted in later books by the Conclave.
Lord of the Rings: The humans and elves vs the armies of Mordor. The closing section of The Hobbit talks quite pleasantly about the goblins being hunted into extinction in the Misty Mountains, without any hint that anyone could have a problem with this (except, presumably, a large number of dead and therefore irrelevant goblins.) Reading the related literature reveals the justification: Melkor, the Bigger Bad who is behind Mordor and all within, is essentially a being of and dedicated to corruption: an all-or-nothing higher being that allows nothing in between.
The Orthodox Jews consider even today the extermination of Amalekites (and their assumed descendants) as a mitzva.
Technically, only the Amalekites were supposed to be destroyed... that is, the rest of the nations were given the option to clear out. Allegedly, one did.
In Codex Alera, the conflict between the Alerans and the Vord. Most of the Vord are mindless beasts under the control of their Queens, which have a genetic imperative to wipe out any other species and expand to consume all. There is also the war between the Vord and the Canim, which ultimately ended with the Canim being almost exterminated, save for the ones that Tavi and Varg were able to evacuate.
Related to the Starfire example in Tabletop Games is the novels based off it by David Weber and Steve White. In addition to the war with the Rigellians as part of the back story there is the war with the Arachnids or Bugs. No attempt at communication succeeds and they view other sentient species as nothing more than food. The only world that is not subjected to massive orbital bombardment is the homeworld of one member of the Crucian Alliance which is liberated the hard way.
Enderís Game:Subverted with both sides due to a major misconception. The buggers, being a hive-mind, didn't realize that humans were individually sentient. When they realized their mistake after killing millions of humans they felt so guilty that they let humanity wipe them out with the exception of one pupal Queen. On the other hand, when Ender destroyed the bugger homeworld, he believed it was merely a simulation and so felt no guilt about his actions until he learned after the fact that he had committed xenocide for real. Card's later Ender books establish a scale of "alienness" between individuals and species, where on the farthest end of alienness it becomes possible to acknowledge that avoidance or xenocide are the only options for interaction between species because they simply cannot comprehend one another. The moral burden is upon the would-be exterminator to make certain there's no way to communicate with (or just avoid) the other species before committing to the extermination war, however.
Black Fleet Crisis: The main villains are the Yevetha, who are your typical Scary Dogmatic Aliens — they're well able to learn Basic and sent someone to meet with the New Republic, fair enough, but they only do this as the prelude to starting a war with it, in which we see that they are impossibly xenophobic and culturally narcissistic; their culture had developed and become advanced with not a single recorded speculation that there was other intelligent life in the galaxy, and First Contact only convinced them that everything else was unworthy vermin which had to be exterminated. (Granted, their first contact was with the Empire, who immediately enslaved them.) Every member of the species was prepared to die fighting, but after winning the New Republic just destroyed all of their ships and left them stranded on their world. Years later, when the Yuuzhan Vong with their similar if not quite as extreme xenophobia showed up, the Yevetha refused to submit and were hunted down and systematically killed.
The Bothans have this as a little-usednote exactly three times in their entire recorded history cultural practice called ar'krai. Every able Bothan is required to volunteer for military service in order to not only slay every last member of the offending group or species, but grind their homeworld to dust. They declare ar'krai against the Yuuzhan Vong after perennial Obstructive Bureaucrat Borsk Fey'lya pulls a Heroic Sacrifice during the fall of Coruscant.
In Last and First Men the Fifth Men kill off the native Venusians without a second thought. Of course, by then earth was dying and Venus had to be terraformed to be inhabitable. Earlier the Second Men used a bioweapon to wipe out the Martians who had been invading earth for several thousand years, but it destroyed their civilization as well.
The Martians in The War of the Worlds have this attitude toward humanity; the humans are too busy being terrified and/or dying to return the sentiment.
In Garrett P. Serviss's unauthorized sequel Edison's Conquest of Mars the humans fly to Mars and cheerfully wipe out the Martians who tried invading Earth. Technically it's an accident, but nobody's really bothered by the extermination of a whole species.
The "Holy War" that annihilated the race of the Ghouls in E. R. Eddison's The Worm Ouroboros is treated that way by the polite nations of the world of Mercury. Lampshaded when Lord Gro tries to mine the genocide for anti-Demonland propaganda and is rebuked by the Red Foliot (a peaceful and mild-mannered chap), who assures him that the extermination of the Ghouls was most certainly a praiseworthy heroic. As the Ghouls were cannibal sea-raiders, it can be inferred that the Ghouls felt no different towards the other races of Mercury.
Monster Hunter International: The vast majority of the undead fall into this as they fall under the "humans are tasty" clause. Many other creatures do as well, like fishmen which like to lay eggs in live human beings. While the government takes this stand in general against most non-humans, they're aware that not every supernatural being are inherently incapable of getting along with people, they just use it for black mail.
Larry Niven's Known Space universe: any war among Pak protectors is one of these. The protector-stage Pak are hyper-intelligent and, at the same time, have incredibly powerful, genetically-hardwired instincts that drive them to fanatically protect their own offspring and close relatives and exterminate anything or anyone else. While the Pak can, and do, wipe out other threatening species, their killer instinct is strongest for other Pak who are not in their own bloodline, because they "smell wrong" (this also applies to their own descendants who are mutants, a relatively common occurrence on the Pak homeworld, which abounds with radiation both as a consequence of being near the galactic core and having loads of nuclear fallout from very frequent nuclear wars). Pak protectors are rational enough to form alliances with non-relatives for mutual advantage, but the very instant there is an opportunity for betrayal, a Pak will take it. The Pak have wrecked their homeworld with constant wars of mass destruction, including nuclear weapons and exotic anti-nuclear countermeasures, and biological weapons (they are quite fond of genetically-engineered plagues which sterilize certain genotypes, as unlike nukes plagues leave behind land and resources which can be seized).
Even when the Pak flee their homeworld ahead of the core explosion, the Pak fleet is in a constant state of war with itself, which often spills over on planetary systems on their path, which the Pak fight to plunder for supplies.
When a Pak Protector comes to one of their lost colonies in the outer edges of the galaxy he finds that the Protectors died off and the colonists evolved into a species that is intelligent enough to build starships before becoming Protectors, but they smell wrong so they must be exterminated. He captures one of the mutants for interrogation and accidentally turns him into a Protector, said mutant learns everything about the Paks, then kills him as a threat to his children. Fortunately human Protectors are also rational enough to realize that unrelated members of their species aren't automatically a threat.
Interesting aversion in the Kzinti: they are vicious fighters who hunt humans for sport, then eat them, but they want to enslave humanity, not exterminate it. The expanded-universe Man-Kzin Wars stories show that the Kzinti are actually spooked by the human concept of total war. A Kzin wouldn't destroy something he would rather conquer.
Three billion years earlier the galaxy had been conquered by the Thrint, a race with the ability to telepathically brainwash any non-Thrint species. The only exception were the Tnuctipun, a race of hyper-geniuses who managed to fake being under Thrint control until they were ready to rise up. The war was one of absolute extermination, ending with the losing Thrint triggering a doomsday device that killed all multi-cellular life in the galaxy.
The Final War with the Melconians in Bolo. The entire war becomes a war of genocide with the only strategy being "kill everything of the enemy's before he kills yours." And the authors do mean EVERYTHING.
The fact that everyone that survived the war was horrified at what happened, with what little remains of both sides agreeing that it was a terrible thing, shows that it wasn't really guilt-free at all.
In Doctor Who, the war between the Thals and the Kaleds would only end with one destroying the other. The Thals "won" by destroying the Kaled bunker thanks to information leaked to them by Kaled scientist Davros - who then turned his creation, the Daleks, on the Thals, thus destroying them as well.
The Daleks themselves are utterly convinced that every single non-Dalek lifeform in the universe must be exterminated; they are also genetically engineered to feel "no emotion but hate", and once engaged in a mutual civil war of annihilation when Davros made a new breed with only trivial, aesthetic differences between them. The Doctor himself varies on the issue; on rare occasions he will try diplomacy or some more peaceful tactic, but on plenty of others he's more than ready to literally Kill 'em All, and is horrified when Joker Immunity kicks in and a handful, or even a lone, Dalek survives.
As was said in the new series episode where the Cult of Skaro first encountered the Cybermen: "THIS IS NOT WAR! THIS IS PEST CON-TROL!"
The Last Great Time War seems to be this as well, from what little we know of it. The Time Lords and Daleks seemed to be out to simply destroy each other, and at some point the Doctor decided that both sides had to be destroyed. There is, however, lots of guilt, not to mention at least some reason to believe the Doctor was out of alternatives; the implacable nature of Daleks had already been shown, and "The End of Time" showed the Time Lords had become just as bad.
The humans on Battlestar Galactica, for the most part, believe this since the Cylons wiped out 99.99999% in the pilot. They will frequently torture and kill captured Cylons because they're "just machines" and don't really feel pain. People who object are typically just written off as incredibly naive or crazy. During the series, however, this attitude decreases to the point where the humans and some rebel Cylons form an alliance against the rest of the Cylons.
Stargate SG-1: the replicators will consume anything and everything to replicate, and the only way to stop them for good is to wipe them out, so the war with them inevitably becomes this. A different type of replicators appear in Stargate Atlantis, and this applies to them as well.
Stargate Atlantis: the fight against the Wraith is generally seen as an us-or-them game as well — the Wraith might not be out to kill all humans, but that's only because they need to keep them as a food supply. Later on, Dr. Beckett develops a virus that turns Wraith into humans, but it wears off without regular boosters and is nigh-impossible to deliver. Even later the Replicators and renegade Asgard force the Atlantis expedition into multiple Enemy Mine situations with one Wraith faction and at one point offer them an experimental treatment that would allow them to live without feeding on humans.
Scorpius spends a lot of time in the later seasons of Farscape trying to convince John that the Scarrans want to wipe out everyone and have to be stopped. Considering that they started wiping out as many species as possible during "The Peacekeeper Wars", Scorpius was probably right.
In Warhammer 40,000, nearly every single race has reasons and plans to exterminate every other race.
This is quite literally the Imperium's standard colonization protocol: drop a few Imperial Guard regiments, exterminate all sentient life on the new planet, ship colonists in. The stone age Tau only escaped that fate thanks to a freak warp storm.
The Tau don't automatically exterminate every species they come across, preferring to integrate and "adopt" other species as they discover them. Still, when they do encounter a species that they determine unfit or unable to peacefully coexist, they will ruthlessly exterminate them. Considering thegalaxy they live in, this proabably happens pretty frequently.
Tyranids exist to eat, breed and absorb the best characteristics of every species that they can get their claws on — only characteristics that facilitate those three imperatives, of course.
Pre-5th Edition, the Necrons served beings that wish to annihilate everything related to the Warp. The Warp is sustained in part by the emotions of living beings. Nothing more needs to be said.
In 5th Edition, they just want to conquer and dominate, but are willing to wipe out all life on a colonized tomb world and also capture a lot of people for destructive scientific experiments.
Everyone to the Orks they are all over the galaxy and come in the millions to quadrillions, and killing them is just like exterminating over sized green vermin that won't go away.
Starfire by Task Force Games: The Third Interstellar War between the Alliance (Terrans and Khanate of Orion) vs. the fanatically racist and warlike Rigelian Protectorate. The Rigelians were determined to wipe out the Alliance, and the Alliance was forced to destroy the Rigelians completely to eliminate them as a threat.
Dungeons & Dragons has the Blood War between the Lawful Evil devils/baatezu and the Chaotic Evil demons/tanar'ri, it's been raging for millenia and is unlikely to end until and unless one or both sides gets totally exterminated. Which is fortunate for everybody else because the fiends could probably wipe out the celestials and everybody else in the multiverse if they weren't so busy fighting each other.
Beholders with even the slightest morphological differences from one another will always try to destroy one another out of pure, uncompromising bigotry.
It's glossed over quite often, but humanity and its allied races are engaged in one with almost every sentient evil-aligned creature in the books. In some cases (such as the illithids, neogi, and vampires), it's a justified trope: only their extinction will spare humanity from a Fate Worse than Death.
Frequent in 3:16 Carnage Amongst the Stars. Because it's usor them.
In GURPS Reign Of Steel this is the attitude of most of the Zonemind computers toward humanity (if not all living things) — and the attitude of nearly all surviving humans toward the Zoneminds. The only major exceptions are the inhabitants of the British Isles, whose Zonemind ignores them so long as they don't get in its way (the British government can compare with the other Zones nearby, so they know this is pretty much the best situation they could have) and the inhabitants of the eastern US, who think their "tame" Zonemind is a loyal servant and protector (they're wrong about the first, and wrong about the reasons for the second).
One of the game's most depraved antagonists was the Seventh Generation, a Wyrm cult that abducts children and uses them as human sacrifices. After ascending the throne, King Albrecht orchestrated a Garou slaughter of Seventh Generation devotees, virtually wiping out the cult.
Total Annihilation: Both factions use this and have to be sure they've wiped the other side out or they'll just rebuild with nanotechnology. The campaign demonstrates this, since you begin with the last commander unit in the last base on the last held planet and tear apart the entire enemy faction from there.
In Mass Effect, the battles against the Reapers' indoctrinated servants, played a few different ways.
The rachni were hunted to extinction. (Deconstruction; they were a peaceful race until they were brainwashed by the Reapers - or possibly the Leviathan.)
The turians and salarians used a Depopulation Bomb to end the Krogan Rebellion. (Defied; the Genophage was made specifically to avoid this trope, and was originally intended by the salarians to be a deterrent)
In general, there's a standing order in Council Space that all AIs are to be terminated on sight. The exceptions are those which are authorized by controversial research companies such as Synthetic Insights. Knowing that every organic in the galaxy is united to kill them without a second thought, many synthetic creatures (such as the geth) adopt a similar "shoot first and ask questions later" policy.
The central conflict with the Reapers is this as well.
The only option (other than Assimilation Plague) in Sword of the Stars before the second expansion added psychology techs that allow a player to force a planet to surrender after just one or two nukes.
In Star Fox Assault the Aparoids are exterminated without a second thought. And in at least some of the possible endings to Command the Anglar are presumably wiped out as well (considering their homeworld is terraformed in a couple endings).
In Ratchet & Clank: Tools Of Destruction, pretty much everyone who brings up the subject considers the Lombaxes the "Saviors of the Universe" for completely wiping out the Cragmites. Granted, it turns out they actually sent them to another universe, but no one else knew that.
Starcraft: the Zerg are a race burdened with a hard-coded biological imperative, instilled by the Xel'Naga, to assimilate and destroy other species. The absolute best that could possibly be done short of true extermination is destroying the Overmind to reduce them to merely very dangerous animals. Turned on its head when it turns out the Overmind intentionally got itself killed to place Kerrigan as its successor and finally relieve the Zerg of this compulsion, and on top of that they may be the only thing standing between the other races and an unknown party that will otherwise destroy all life in the galaxy — the Overmind executed this gambit because otherwise the Zerg would destroy all other life, then be destroyed in turn by this new threat.
The Human-Covenant war starts out this way in Halo, the covenant goes to far as to completely destroy each Human planet they encounter. That is, until the Elites get betrayed by the prophets. And it later gets revealed the war was a cover up. Played thoroughly straight with the Flood.
The Human-Locust War in Gears of War is one of these. The Locust want to exterminate humanity so they can have the surface of Sera, and the humans want to exterminate the Locust in self-defense. The Lambent also get in on this when they show up, making it a three-wayGuilt-Free Extermination War.
The war against the Kreegan in Heroes of Might and Magic III: Armageddon's Blade becomes this after Erathia drops out. The remaining anti-Kreegan forces are well aware that the 'Devils' are a severe threat to the world (even if they aren't aware of the full scope of the threat), and finishing the war to the bitter end is really the only long-term option, while the Kreegans built the titular Armageddon's Blade to burn the world. Even before Erathia dropped out, the problems the nobles had with a campaign of extermination wasn't the extermination, but rather the cost in troops and gold.
The gameplay of the Warcraft games generally play this straight. To win you typically have to annihilate the enemy force down to the last peasant worker and farm and they'll do the same to you if given the chance.
World of Warcraft's quests often boil down to this. There are some specific examples in the story.
Used in Cataclysm with the evil Black Dragon's being rendered extinct by Wrathion; apparently the only uncorrupted Black Dragon.
Mists Of Pandaria plays this straight with the formerly neutral Zandalar tribe and the Mogu.
Operation Final Fury in X3: Terran Conflict is a military operation between threeseparateraces to completely wipe out a hostile race of Bee People - the Kha'ak. The player helps out as a mercenary, and is the one to kill off the Kha'ak Hive Queen. By the time Albion Prelude takes place, the Kha'ak are totally absent - the only sign of them are their abandoned ships drifting through space. Which conveniently allows the Argon Federation to focus its resources into trying to kill off the Terran State, which they start by blowing up the Torus Aeternal defense station which encircles Earth's equator, causing it to de-orbit and kill tens of millions. The Terrans respond in kind by obliterating any Argon ships and stations they come across.
In this amazing game of CivilizationII which has been running on and off for the past ten years, the world has descended into a nightmarish dystopia which proves undeniably that War Is Hell. There are three main factions, the Americans, the Vikings and the Celts, who are locked into a brutal, genocidal, fight to the death and have been for the past 1,700 years. All attempts at peace or even Enemy Mine situations fail miserably with the AI sides betraying and attacking the player and each other scant moments after a cease-fire or agreement is signed, the constant nuclear war has killed 90% of the world's population and reduced the Earth's surface to radioactive swampland, the polar ice caps have melted 20 times so far, and large cities and improvements are a thing of the past because all available resources go to fueling the war effort and any city that does grow large is likely to be nuked.
In Guild Wars Prophecies this is the nature of the war between the Charr and humans. The Charr are all too willing to wipe out all three human nations on the continent and use the survivors as slaves and entertainment while the humans view the Charr as little more than dangerous animals. Even after the Shamans were overthrown, the Charr persisted in a war to drive out the remaining Ascalonians for over two centuries. It took the appearance of the Elder Dragons to stop the fighting and some hardliners on both sides have decided to keep the war going.
The Mursaat were willing to kill anyone who refused to submit to their control, resulting in an all-out war between the White Mantle and the free people of Tyria. In the end, nearly the entire Mursaat race was exterminated along with the majority of the Mantle.
The Highbreed from Ben 10: Alien Force were determined to wipe out every other life form in the universe, convinced they were more "pure" than every other organism. Pretty much every other species had caught on to this, and didn't hesitate to destroy Highbreed in return. Ben found a way to Play With this trope and resolve the issue: he used the Omnitrix to graft alien DNA into all the Highbreed, leaving them no longer "pure" Highbreed and removing the rationale for their Extermination War. In a sense, they were wiped out as Highbreed to resolve the conflict; they just got new lives as hybrids instead of having to die en masse.
Pathogenic (disease-causing) organisms (bacterial, viral, fungal and parasitic) vs. humans for the most part - at least on our side. The diseases are mindless of course so they have no motivation beyond reproducing themselves and infecting hosts in order to do so; they rely on some of us existing for their survival. (Orson Scott Card's Children of the Mind raised the interesting question of what could be done if we discovered a sentient virus - could coexistence be possible?)
The first disease we've been able to exterminate was smallpox. The only surviving samples are around for research.
The fact that smallpox was exclusively a human disease, not something humans contract from animals or their surroundings, made it much more vulnerable to vaccination campaigns than most pathogens.
On 8 August 2011, the United Nations held a ceremony declaring rinderpest eradicated - the second disease to be fully wiped out.
However, this attitude is frequently taken too far with all bacteria being regarded as enemies, when a number are neutral and crowd out harmful ones and others are outright beneficial. This is a problem with excessive use of broad-spectrum (i.e.: useful against most bacteria, not just pathogenic ones) antibiotics - they're extremely useful and save a lot of lives, but shouldn't be used for minor illnesses because they also kill off the beneficial bacteria that live in your gut. There's also the problem of antibiotics selecting for bacteria that are resistant to them, meaning we need to constantly keep developing new antibiotics to deal wit the resistant ones.
Poliomyelitis (infantile paralysis, or "polio" for short) is almost exterminated, occurring only in some war-ridden regions. Good riddance - for apparent reasons.
Not a germ, but closely related to one. The small, silvery mosquito called AŽdes aegypti (beforehand, Stegomyia fasciata) used to spread yellow fever in the Americas. It has been eradicated from the Americas. (A silent nod to DDT...) More on how yellow fever destroyed Memphis after the Civil War is at http://www.americanheritage.com/content/epidemic
Also questionable, because mosquitos do serve important roles as low-flying links in any number of food chains. Exterminating them in their entirety, as opposed to controlling their populations, could have far-reaching effects that haven't even been considered, even aside from the collateral damage things like pesticide cause. Getting rid of the Anopheles mosquito - the type that spreads malaria - could be very useful, though, and scientists are looking at ways of achieving this, as well as alternative ways of making it incapable of transmitting malaria.