Mobile Suit Gundam (original Universal Century timeline): The Principality of Zeon launches a war with their mobile suits (at the time, a new technology). At the start of the first series, the Federation has just produced the RX-78 Gundam, a Super PrototypeHumongous Mecha with the armor and weaponry roughly equivalent to that of a battleship. By the end of that war, only a few months later, Zeon has begun mass producing mobile suits that are almost even with the Gundam. Seventy war-filled years later, the Victory 2 Assault Buster Gundam is 3 meters shorter than and half the weight of the RX-78, and boasts an inertialess drive system, a force field and more firepower than every Mobile Suit from the One-Year War put together.
Mobile Suit Gundam 00 has this happen right around the end of the first season and takes off from there. By the end of the second season, they've gone from mostly present day levels of technology to fleets of battle ships, armies of superpowered mechs, a gigantic space station with a super laser, and a Mobile suit capable of going through matter and connecting people's minds. The movie, though not technically an example, essentially continues this process to... well escalate.
Mazinger Z: Throughout the series, the title Humongous Mecha has to be constantly upgraded and endowed with new weapons and capabilities in order to battle Dr.Hell's increasingly powerful Kikaiju. Of course it drove Hell to create still more dangerous Robeasts and when Mazinger Z finally could not catch up, it was replaced with an entirely new robot, Great Mazinger.
In Code Geass, the first example of Real Robot technology was used in combat seven years before the series, consisting of ground-based Knightmare Frames armed with machine guns, recoilless rifles, and cannons. At the start of the series, most of these have been replaced with a newer generation of Knightmares, but they are still limited in their abilities. The second episode introduces the first Seventh-Generation Knightmare, a Super Prototype with experimental weapons and technology, but still ground-based. New technologies are introduced as the show's first season progresses, including flight packs, radiation waves and hadron cannons.
There are indications given that most of this was already in development and fairly refined. The initial Super Prototype mentioned had been completed for months and its main scientist was begging for a test run from a very resistant military. The energy weapons, shields, and flight capability all existed, but only for Flying Battleships. Apparently in that intervening year, the performance of the first Super Prototype burst a dam of innovation and miniaturization.
Gundam Wing has a bit of a Lensmen quality to its mobile suit development. Initially the Leo mobile suit is a formidable weapon especially in the hands of a competent pilot. In the first episode we even see Zechs take out Heero's gundam using nothing but a Leo (albeit sacrificing the suit in the process). Soon the Taurus comes out, and the series is dominated with images of Taurus' tearing Leos to shreds. Then comes the Virgo, a much more innovative mobile weapon which is seen tearing Taurus' to shreds (and Leos too). The culminations of this arms race are Gundam Epyon and Wing Gundam Zero, both capable of massacring whole armies of Leos, Taurus', Virgos and basically every other mobile suit seen before them.
Except that Tallgeese and Wing Zero are twenty-year-old designs, so you can't fairly call Wing Zero a "culmination" and while Treize did use a variation of the ZERO system for Epyon, he didn't really put any new technologies on it. And remember, the original five Gundams are deliberate downgrades of Wing Zero.
This is an interesting case because the Tallgeese was the original mobile suit in-universe. However, it had none of the safety precautions built into it. The sheer G-force it put out was capable of killing it's pilot so it was mothballed as a museum piece. The Leo is basically the Tallgeese stripped of everything but the basic humanoid shape, allowing people to use it safely. In the same vein Wing Zero used a interface that allowed the pilot to control the robot with their mind, which allowed the pilot to multi-task and have faster reflexes because there is zero delay between issuing the command from their mind and it getting to the controls (rather than having the brain move the arm, then moving the controller). Unfortunately the connection was too perfect, causing too much feedback to the pilot, usually resulting in insanity. The Arms race was less of developing more powerful weapons, and more about developing controllable ones.
Tengen Toppa Gurren Lagann does this with the title Humongous Mecha. The heroes start out with a little robot the size of a car (the Lagann), but by the end of the series, becomes the nucleus of a gargantuan battle beast that can hurl galaxies as shurikens. It also does this with awesomeness. Hand Waved on the grounds that the entire universe is powered by Spiral Energy, which causes the scale of events to spiral outward like this. Of course, it helps that every major upgrade save the last one is achieved not through actual technological development but rather by stealing technology from enemies or finding technology of the defeated previous Spiral Warriors. Indeed, it's heavily implied that at least some of it isn't even "real" technology at all, but rather Spiral energy made manifest.
Gun Buster engages in some of this as well, going from fairly sci-fi standard space vessels and Gundam-ish robots to using Jupiter as the core of a Black Hole Bomb to destroy the center of the galaxy to wipe out the race that wants to kill humanity.
There's an absolutely hilarious parody of this in the fifth episode of the first season of Rozen Maiden. It has to be seen to be believed.
To be fair, the Vajra are another species entirely, not some manufactured weapon. As far as actual Valkyrie designs go though, not much has really changed in the fifty-or-so year time span besides a shift to energy-based weapons and some miniaturized equipment.
GaoGaiGar escalates rapidly, especially when the show starts Growing the Beard. When the series starts, a single monster mostly threatens a skyscraper, the enemy spends most of it's efforts to make a single Zonder metal plant, and at the end of the arc, nearly transforms 75% of the city into one. By the end, nearly every monster is its own plant, and the final battle is fought against the moons of Jupiter
The villains of Gao Gai Gar Final takes the logical next step by creating an evil duplicate of the Solar System, powered by a sun made of G-Stones. To which the heroes respond by revealing what they'd built to deal with threats at the level of the aforementioned battle on Jupiter: a a hammer that crushes the sun.
This sequence happens repeatedly in the universe. Al-hazard destroyed itself; survivors settled Belka. Belka destroyed itself; survivors settled Midchilda. Midchilda... almost destroyed itself, but turned back in time. So far.
And the race is re-started again in Magical Record Lyrical Nanoha Force with the Dividers able to render useless any magical weaponary showed at the time thus forcing the TSAB to take a risk by making weapons that convert magic into conventional energy to power up physical attacks, getting closer and closer to breaking their once stone setted ban on mass-based weaponary.
Getter Robo starts off with a single Humongous Mecha fighting monsters, to every nation on Earth having them and engaging in conflicts of World War proportions, to epic wars in space between galaxies. The action grows in scale and the mecha in size rapidly from there, and peaks at the point where one of the mecha is larger than galaxies and can stand toe-to-toe with God.
Overall, this series is something of a Deconstruction of the idea. The main characters are trapped in a Lensman Arms Race because the Getter Rays, the energy of evolution, keeps pushing them forward regardless of the consequences for the universe. The antagonists are fighting them to prevent this, but by attacking humanity they only make them stronger. This results in a vicious cycle of increasingly escalating power that will eventually destroy the universe.
This trope turns out to be the real reason Claymores and related demonic hybrid beings are developed in Claymore. The nation is gearing up for a war with another nation that has successfully militarized dragons of all things.
Zoids would dip into this from time to time but the most prominent example would be how the Ultrasaurus ended a war in a few months but the war had lasted 50 years. A few years later the Death Saurer was introduced and destroyed all opposition including the Ultrasaurus only being slowed by terrain too mountainous for its bulk. A few years later the Madthunder was introduced and won the war in a year for a country that had been pushed to the brink.
Transformers Animated comic "Everything Must Go". It is based on the Dr. Seuss book The Sneetches, just replace the Sneetches with Lugnut and Blitzwing, the merchant with Swindle, and the stars on their stomaches with every other weapon in Transformers mythos. This ends with the destruction of New Kaon, after which Lugnut and Blitzwing catch on and rip Swindle apart.
Terrifyingly, such a weapon could have been built in Real Life during the Cold War, although neither side will admit to ever having done so.
Actually, reports vary on whether the Russians' actual Dead Hand system is human-controlled or fully automatic.
And a nuclear holocaust can't stop the arms race, because now the Americans have to move people into mine shafts as they wait out the radioactivity on the surface. Fearing the Soviets will move more people into mine shafts and have superior numbers when they emerge, Buck Turgidson declares, "We can't allow a mine shaft gap!"
In the film The Men Who Stare at Goats, and the book its based on, and in real life, the United States Army started research on new age and psychic powers because they heard Soviets were researching those things as well. The Soviets supposedly started the research because they heard a rumour the Americans has started research...
This is going on in the Marvel Cinematic Universe. Humanity's gone from not being worth anyone's notice to rather shocking. When the Tesseract fell into Earth's hands, that got the attention of a lot of races that didn't notice them before. When Earth drove off the Chitari in The Avengers, that really scared them. We just got Thanos of fucking Titan interested in us.
In Iron Man 2, the US government wants to nationalize the Iron Man tech because they're afraid other nations will copy and mass-produce it before they can. Stark counters with evidence that enemy nations' attempts at this are failing hilariously, but nonetheless shows that they're trying. Then Ivan Vanko shows up and proves that Tony's not the only genius who can do amazing things WITH A BOX OF SCRAPS, adding fuel to the government's arguments.
Lensman also gave us the Sunbeam; a whole star system altered to function as core, coil and vacuum tubes for a beam that directs the full power of the star into a fleet- and planet-annihilating beam. Lensmen and their rivals, Boskone, routinely flung planets at one another at relativistic speed in lieu of normal relativistic projectiles found in other novels. By the end they develop a way, both sides, to create wormholes that allow them to fire FTL planets at one another from intergalactic distances. Nevermind the fact that, originally, their "Super-Mauler" class battleships were created to kill relativistic planets in battle, and by the end both sides were producing them by the tens of millions and using them as frontline battleships. They mass-produced Death Stars! Ironically the Super-Maulers proved ineffective...because the Boskone forcefield tech was amped up before they were deployed, ergo they simply started using them as battleships instead. The Sunbeam was considered a stop gap against relativistic planet bombardment until they developed something better.
The FTL antimatter planetoid projectiles mentioned in the opening paragraphs? Yeah they start mass producing those as well. Including smaller ones designed to be launched from bomber squadrons, and whole fleets of them to be used as interstellar bombardment against enemy planets and star systems. This was also considered a minor footnote by the end, where their FTL planets launched from wormholes could destroy star systems from intergalactic distances.
The Lensmen at one point were thrown into another dimension where the laws of physics are different. After finally figuring out how to return to their home dimension, they went back to the other dimension and modified two planets to be thrown at Boskone. When they did, the "foreign" planets hit the Boskone planets at 15+ times the speed of light.
A second, in some ways even more ridiculous, example from EE Doc Smith is his lesser-known Space OperaSkylark Series. By the final novel in the sequence, our heroes destroy two entire galaxies by teleporting every star from one into the close vicinity of every star in the other, causing each pair to collide and go nova, meanwhile teleporting every non-hostile world in the area to safe orbits around stars in a third galaxy, all while they themselves are safe in yet another galaxy entirely...! And all this only four books after the same human protagonists discovered space travel!
In both the Lensman and Skylark series, Smith combines fast evolution of weapons with a crazily short research and development cycle. The antimatter bombs go from theory to practice in a few months. In his proto-Lensman novel Triplanetary, agents of the Triplanetary fleet refit their own side's guided missiles to accept guidance from a totally new, recently-discovered means of communication... in the middle of a battle. And it works. Of course, the crazily short R&D cycle was something of a commonplace in all the pulp science fiction of that era, and is echoed by accomplishments in WWII a conflict which started with prop-driven biplane fighters, 3- and 5-tonnes machine-gun armed tankettes and a general level of technology not much distanced from WWI and ending (six years later) with the battlefields bristling with 55-ton armoured behemoths, jet powered fighters and bombers, flying bombs, ballistic missiles and nuclear bombs. "Doc" Smith was a Ph.D chemist who spent WWII developing explosives for the U.S. goverment, and most of the Lensmen books were published post-war.
In Skylark, the Lensman Arms Race only really gears up when the protagonists encounter a very ancient civilization whose Hat is Science. They have worked out pretty much everything thousands of years ago... too bad they didn't have any of the atomic catalyst until the heroes showed up...
The Honor Harrington series by David Weber, though nowhere near as over-the-top as Lensman. note Much of the "new" tech is actually existing tech being used in new ways; the realism of this is hotly debated. The series started out as a Recycled In Space retelling of English and French naval battles of the Napoleonic Wars, and the technology advances mirror actual advances in naval warfare. Cannons to missiles. Armor ("bow and stern walls" energy shielding) to aircraft (LACs) to radio (faster-than-light comms) to guided missiles (project Ghost Rider). Submarines are creeping in with the Mesans' new spider drive.
As the series progresses the trope becomes stronger: the Mesans have revealed two new super-duper space drives, an entirely new biological "mind control" weapon, and that's just the first few things we've seen so far coming from their centuries-long supersecret R&D program.
Weber's Starfire series showcases realistically depicted arms races spurred on by the current conflict, with specific technologies and tactics being designed to counter the enemy's latest gimmick, while at the same time still managing to follow the respective races' (often) wildly divergent military doctrines. This seems to be Author Appeal for Weber; it also shows up in a Giving Radio To The Romans set-up in the Safehold books, and in his standalone novel The Excalibur Alternative.
Safehold in particular is all about invoking this trope, as the main character Merlin Athrawes tries to bring the Lost Colony of Safehold out of its Medieval Stasis by helping introduce innovations to one country and prompt the rest to try and catch up.
Subverted in the Arthur C. Clarke short story Superiority, where the side which tries out the new technology in battle (without adequate field tests) loses. This was a clear allegory for World War II and the German investment in "superweapons" as compared to the Allied investment in, for lack of a better term, MnogoTanks (for both the US and USSR). Lesson: In industrial war, industrial capacity is more important than the quality of the weapons. Unless, of course, your weapon is The Bomb...
Computer War, by Mack Reynolds, is similar to Superiority. For example, the advanced side uses alarms that can detect laser fire to help guard their buildings — which are useless, as the saboteurs use bows and arrows to kill the guards. Also, although this side has a massive conventional military advantage, the weaker side is winning by fighting guerrilla-style, and only in easily defensible terrain (mountains, swamps).
Played with in Philip K. Dick's The Zap Gun, where a pair of weapons designers, one on each side of the Cold War, are continually coming up with what are ostensibly new weapons. In reality, though, everything they come up with is immediately repurposed into harmless knick-knacks. This helps keep the Cold War cold, but proves disastrous once aliens invade, and the world is defenseless. They end up getting the aliens to leave by getting them addicted to a video game.
In the German pulp Sci Fi series Perry Rhodan (started in 1961 and still running), the story started with the title character, Perry Rhodan, being the first human to land on the moon. 10 issues in, he was commanding an interstellar cruiser, and in another ten issues in he achieved immortality.
More than 2000 issues followed and stuff grew grander and grander in scale: Cosmic Powers of Order and Chaos, called "Kosmokrats" and "Chaotarches" by the less-advanced races, are forever fighting for supremacy, using mortal species and even ascended beings as chess pieces because they cannot interfere directly. The Chaotarchs try to literally unmake the laws of physics and return the multiple universes to a state of ur-chaos where they can thrive, while the Kosmokrats seed life and sentience throughout the galaxies and try to defend the "cosmic code" from tampering.
While the Kosmokrats appeared to be the Good Guys in the beginning (sponsoring space-faring races, granting immortality to certain exceptional individuals to further their plans) it became more and more apparent that they behaved like the Vorlons from Babylon 5 in that they treated "lesser" races like chess pawns, and reacted badly to anyone trying to leave their service. As they claimed, they saw a bigger picture. Existing outside time and space, these transcendent entities were no longer able to imagine or sympathize with the plight of mortal races, even though they had started out as whole races of mortal species eons ago.
Turns out the cosmic superweapons of the Kosmokrats were often just as destructive as those of the Chaotarchs; in one instance, servitors of the Kosmokrats were ordered to destroy a whole galaxy (and all civilizations in it) down to the subatomic level rather than seeing it fall into the Chaotarchs' hands. Somewhere in midseries, Perry Rhodan showed them the finger in parallel to what happened in Babylon 5.
Stephen Baxter's Ring: The Xeelee use cosmic strings to build a Kerr metric with which they can escape into another universe. This structure (the Ring) is so massive that it is pulling all galaxies for quite some distance towards it, at high speed. The Xeelee's antagonists, the Photino Birds, go one up on this by arranging galaxies around the Ring to form a resonance cavity that will shake the Ring apart.
Belisarius Series: The series starts out with fairly normal armies for the late antiquity or early middle ages. In particular, heavy cavalry is hugely emphasized. Thanks to Alien Space Bats, however, they start moving up the tech tree very rapidly. It starts with primitive gunpowder weapons such as handheld rockets and siege cannons. By the end of the series, they're using breach mounted rifles, ironclads, and radio.
In an alternate future where only one of the two sides comes back to the past, we also see the bad guys developing tanks. It didn't happen in the main series timeline because they started the war far earlier, so the bad guys didn't have as much time to prepare.
Subverted in Norman Spinrad's The Iron Dream. The body of the book is (ostensibly) an award-winning novel from an alternate universe where Adolf Hitler migrated to the United States and became a science fiction writer. Over the course of the novel-within-the-novel, the hero and his cohorts develop (or reinvent) technology at an astonishing pace until a final confrontation with the villain unleashes nuclear weapons and forces the heroes to invent cloning technology and interstellar space travel in no time flat. The book deliberately takes advantage of established tropes in science fiction and fantasy to try and force a comparison with Nazism. Although it is patently satiric, some readers have taken it at face value (including the American Nazi Party), thus subverting the subversion.
In a rare fantasy example, The Wheel of Time. The first book has fireballs and single bolts of lightning as enormous feats of power, and the idea of facing down 1500 Trollocs is an earth-shattering prospect. By the book 11, we're at uses of magic that can melt the planet if performed incorrectly, and an attack by 100,000 Trollocs is considered an assassination attempt.
Unlike many examples of this trope, though, it was planned from the start. The story revolves around prophesies of The End of the World as We Know It, and the Distant Prologue of the first book features a channeler creating a volcano by accident, so the potential was there all along.
In Alan Dean Foster's Humanx Commonwealth universe, this occurred between two Precursor races in the series' Back Story. The Tar-Aiym were individually powerful, warlike, and technologically advanced; while the Hur'rikku were prolific and persistent. Panicked by the Hur'rikku threat to use their planet-destroying anticollapsar weapon on Tar-Aiym worlds, the latter embarked on a hurried program of weapons development. The program eventually led to the release of a "photonic storm", a plague that travelled from world to world, wiping out all life forms more complex than single-celled organisms over a vast region of the galaxy, including the Tar-Aiym and Hur'rikku themselves. 500,000 years later, this region becomes known to the expanding Commonwealth as the Blight.
It later turns out that the Tar-Aiym constructed, but never used, an entire artificial planetoid constructed entirely out of Krangs, a single one of which is enough to destroy a fleet and the combined might of all of them is sufficient to rip a hole across spacetime that can destroy entire star systems. And when that weapon proves ineffective against the Great Evil, The Hero Flinx has to go looking for an even bigger one built by an even older race.
In The Eschaton Series by Charles Stross, this is slated to happen at some point in the future. Albeit one-sided as Eschaton, in a simple display of its power drew humans from all different time periods and scattered them across the stars. The other side in this arms race is a Nazi cult that uses mind uploads to store knowledge. Somehow in the future they're able to get power fast enough to avoid being warped into a blackhole. The "present" of the series shows that whatever they developed, it was stronger than Eschaton and that it was achieved pretty quickly in order for it to beat Eschaton's omniscience and omnipresence.
Something of a subversion in the Frank Herbert short story Cease Fire. The war is in something of a standoff, with both sides using small manned stations. A techie invents a device to detect and remotely detonate the power supplies in these hidden bunkers, ending the fighting at a stroke. The military top brass are deeply upset at this discovery, because they know that Humans Are Bastards and destroying the effectiveness of this relatively clean style of warfare will only mean that in a generation or two humanity will escalate to something worse in order to wage war. They're proved right by the afternote, which implies that biological weapons became dominant in the next major conflict.
Briefly referenced in Small Gods, with regard to the Moving Turtle (a steam tank designed by the young philosopher Urn). In the event, though, it doesn't come to that, partly because the Turtle doesn't work (Lu-Tze can spot something that could change history, and takes steps) and partly because Om forces the other gods stop the war altogether.
"What if we do keep it? It'll be a... a deterrent to other tyrants!" "You think tyrants won't build 'em too?" "Well... I can build bigger ones!" Urn shouted. Didactylos sagged. "Yes," he said. "No doubt you can. So that's all right, then. My word. And to think I was worrying."
Magic: The Gathering novel The Brother's War has the title war between two nations consist of an increasing arms race mostly fueled by the title Brothers. Starting out with a few scavenged and re-fitted machines left behind by the Precursors, and ending with giant mechanical dragons, flights of Da'Vinci-esque fliers, robot soldiers, combining mechs, and shapeshifting clay golems.
Kurt Vonnegut wrote a book, Cat's Cradle, in which something has been invented which could totally wipe out all life on Earth. Try to guess whether or not the two powers involved in the real life nuclear arms race of that time fall over one another trying to be the first to acquire it.
And of course, it's an insane 3rd party that accidentally unleashes the thing, destroying the world, illustrating the inherent danger and instability of any Mutually Assured Destruction scenario (like the cold war).
David Wingrove's Chung Kuo novels have a period of this, after Stefan Lehmann's attempt to conquer Europe through brute strength stalls. The front line in his war against Li Yuan's forces becomes suicidally uninhabitable as both sides seed no-mans land with increasingly deadly drones and smart mines, and the stalemate is only broken when the Big Bad Howard Devore arrives and tries to annihilate all life on Earth.
The Star Trek novel Final Frontier by Diane Carey (not the novelization of the movie) claimed that the Romulans developed the cloaking device because Enterprise's first captain (with Kirk's father as his second-in-command) tricked them into believing the Federation had one.
David Drake's Northworld trilogy includes a planet of "giants" (basically, people who are 5 feet tall and five feet wide, strong as can be, smarter than normal people; it's based on Norse myths) who live in isolated citadel-cities, and who are constantly at war with one another, building more powerful weapons, tanks, etc. The engineer, Ritter, is a super-genius who could win the war for his citadel yesterday, but he only designs slightly better weapons because if he did it wouldn't be fun any more.
Explicitly referenced in Larry Niven's Down in Flames, a tongue-in-cheek outline for his lastKnown Space novel. "Before it's over, we'll need billions of human protectors. It's a Flash Gordon/E.E. Smith war, with superior Tnuctip technology battling tools and weapons worked up on the spot by a billion Dr. Zarkovs. [...] I'm not strongly tempted to write this story. The scale of things near the end gets bigger than I like."
Live Action TV
John Criton does this single-handedly in Series/Farscape with his wormhole research. First he learns how to enter and fly in wormholes, from there he becomes an expert on discovering them when they open, then he learns to make wormhole weapons, the first can destroy a single ship by putting one opening in front of the ship and another in the corona of a star. The second and final wormhole weapon of the series is a black hole which nearly destroys the armadas of the two most powerful empires in the known galaxy. While this is happening Criton claims that the black hole could potentially destroy the entire galaxy.
Subverted in Doctor Who serial Genesis of the Daleks - the war between the Kaleds and the Thals has been going for a thousand years. It started with nuclear bombs and chemical weapons. By its end, the two sides were using a mish-mash of lasers and WWII-era weaponry due to resources being diminished over the course of the war. In the end the Kaled scientist Davros turns the "environmental suits" he was working on into the Daleks, who exterminate both sides.
Star Trek: Voyager followed this trope to some extent in their clashes with Borg vessels. At the end of the third season of Star Trek: The Next Generation, which Voyager spun off from, a single Borg cube destroyed the bulk of the Federation's fleet and nearly destroyed the Earth. By the middle of Voyager, the title starship was single-handedly blowing Borg cubes out of space — and they had to create the technology to do so while stranded 70,000 light-years away from the Federation.
The Cube in TNG blew threw a fleet of 40-ish starships; not the bulk of Starfleet, but the ships close enough to stop the cube. (That said, the difference between Wolf 359 compared to Voyagers battles are greatly out of balance.)
In Stargate SG-1, it is initially a miraculous feat for humanity to figure out how to even operate a piece of advanced alien technology, namely, the Stargate. This turns out to be a risky move as they run into the Goa'uld, an egomaniacal alien race which rules various interstellar empires by using their advanced technology to pose as gods. Early on in the show members of Star Gate Command have to use ingenuity to adapt modern day weapons and what little alien technology they understand into methods of combating the much more advanced Goa'uld.
In less than a decade, the SGC goes from special ops guerrilla tactics, and firing missiles through the stargate, to commanding a fleet of home built interstellar starships. Most of this advancement happens after season 6 or so when Earth's first starship, the Prometheus, is completed and the US starts making squadrons of X302 space fighters.
Replicators, however, take the cake. This race of sentient lego bricks which form into spiders and endlessly build more of themselves were a threat so advanced even the Asgard, a race that could pimp smack the Goa'uld, have to devote most of their resources to fighting them. At first it is mankind's more primitive way of thinking that allows us to stand toe to toe with this menace. Since their replicator blocks are based on "kiron" pathways, an energy particle humans had not even discovered, SG1 decided the best response to a replicator threat was a 12 gauge shotgun. This seems to work until the Asgard decide to screw it up by trapping the replicators in a time dilation field. Their stupidly brilliant plan backfires when the replicators are able to reverse the time dilation device just before it activates and advance thousands of years, creating new humanoid replicators (made up of nanobots instead of cells) that are immune to shotgun blasts! Not to worry though, because thanks to SG1 the device was reset properly, freezing the replicators in time just long enough for humanity to learn how to make a weapon that destroys kiron pathways.
At about this time, the Goa'uld start to look pretty lame with their highly inaccurate staff weapons and complete ignorance of camouflage. The writers decided to have the replicators wipe out most of the Goa'uld and throw in a new opposition, the Ori. Unlike the Goa'uld, who were in fact just parasites that controlled humanoid bodies and used technology to pose as gods, the Ori basically are gods. They're incorporeal, immortal beings that gain power from people worshiping them. Their followers have super stargates that can transport huge fleets across intergalactic space, and their ships and weapons are capable of curb stomping anything seen in the previous seasons of SG-1. Fortunately the forces of Earth have a solution: they create weapons that can kill immortal incorporeal beings.
Power Rangers RPM had one of the more obvious and implicit examples: it is directed stated that, due to the robotic nature of Venjix and his forces, the Power Rangers' weapons will eventually become completely useless. As the series progresses the Zords they start with go from being able to deal with the monsters directly, to becoming inevitably obsolete in a few episodes, and likewise every few episodes a new Megazord, batch of Zords, or both is added to compete. By the end, it becomes a major plot point that Venjix is going to outmaneuver them if left to grow unchecked.
In a reverse of the above, Power Rangers Zeo explained early that the Zeo powers were based on, basically, a perpetual energy machine: i.e., they continue to get stronger over time. While the Machine Empire, led by King Mondo, prove to be their equals or betters at first by the arrival of the Gold Ranger this is completely the opposite. The addition of a new Carrier Zord, the Warrior Wheel, Super Zeo Megazord and various other gadgets basically seals the Machine Empire's fate. By the end of the series, the Zeo Rangers were fighting Mondo directly without the need for Zords at all in the final episode...something that would have been literally impossible at the beginning. Unfortunately the Zeo powers were lost, and to say the least they got kicked back beyond even square one for the next season, Turbo.
This has happened to professional wrestling as a whole, although it has been most drastically visible outside of WWE in the past decade. Moves that were considered devastating once-a-match nearfalls in the 70s, like the piledriver and the vertical suplex, have since become mundane moves. The powerbomb, considered the scariest and most dangerous move in the business when it was popularized in the mid 90s, is occasionally used as a mid-match move by modern wrestlers like Samoa Joe. WWE eventually took measures to curb this by implementing a "safe style" in 2005 in order to minimize the health hazards of the more dangerous moves being invented (as well as ensure that classic finishers like the Stunner, choke slam, and power bomb still looked effective), but the wrestling world outside WWE continues to invent crazier head drops and more spectacular flips. This has the double effect of making older moves look weak and threatening wrestlers' health.
The Dragon Gate promotion has been the worst offender in recent years. CIMA's Schwein went from instant victory to repeated nearfall in just three years; Naruki Doi's Bakutare Sliding Kick was reduced to The Worf Barrage; and SHINGO's Last Falconry was replaced by an upgraded version that failed to keep opponents down (the renamed Original Falconry became a low-level impact move) while his death finisher, MADE IN JAPAN, suffered such Badass Decay that SHINGO's rival BxB Hulk was able to survive three of them.
All Japan Pro Wrestling has a particularly awful case, extending to its splinter-rival, Pro Wrestling NOAH. The old finishers like the Tiger Driver and Folding Powerbomb just didn't cut it, so new, more vicious and head-dropping moves were invented to be the real finishers in big matches, so that the old finishers were now recurring moves. Then worse finishers got invented, leading to huge death-drops like the Burning Hammer and Tiger Driver '91. This is believed to have led to the eventual death of legend Mitsuharu Misawa in the ring, as his neck could no longer take the punishment.
Although it's often possible to win through peaceful means such as election or Ascend to a Higher Plane of Existence, this is usually what happens in 4X games round about the midgame. In Sid Meier's Alpha Centauri, for example, it's entirely possible to start a vendetta with a Chaos Gun (level 8 offense) and have a Quantum Laser (level 16 offense) by the end, and that's if the vendetta finishes relatively quickly.
This is a key part of all the Civilization games. At the beginning of the game you are basically throwing rocks at each other and by the end you are using stealth bombers, atomic bombs and giant mecha.
This also occurs within, and over the course of, the X-Com games. The first game starts on New Year's with a group of soldiers, rifles, and rocket launchers. They've got lasers before the end of February. Around April, they're using alien plasma cannons that can burn through almost anything, and wearing armor made out of the hull metals of captured UFOs. Around the end of the summer, they're wearing Powered Armor and firing guided missiles that are even more powerful. Around October they can fly, and they ride a ship that can travel to Mars. Around November, at the latest, they're all psychic. The enemy scales to match. The second game features much the same thing, but underwater (it's basically a carbon copy of the first game, so no advancement is expected). Chronologically, we then travel to The Frontier(TM) region of space and by the end of the game, we can travel through black holes to reach pocket dimensions, and have a bomb that can force supernovas from suns. And then Apocalypse just goes nuts.
If series like Gundam and Getter feature this, surely putting the two of them together in Super Robot Wars games, along with a ton of other mecha, leads to this in spades. Let's put it this way: In one game, you get the Zeta Gundam (fresh off the production line, plans drawn less than a month ago) and the mass-produced version of the Zeta Gundam, the Re-GZ, at the exact same time. In Alpha Gaiden, Kamille Bidan comments that Heero Yuy's Wing Zero must have been developed before mobile suits were even invented. This isn't counting the fact that the V2 Assault Buster Gundam, mentioned above, is rolled out of the factory within a few years of the original RX-78 Gundam. So Yeah.
This is also found in Galactic Civilizations II. In fact, since one of the game's major gimmicks is the detailed customizability of the player's units, a great deal of the game is spent not just advancing up the (broad) tech tree, but also finding new and effective weapon and defense combinations for individual ships. The expansion packs, of course, add even more ridiculous technology, until by the end of the last expansion, you can build your own customized Death Star.
EVE Online is heading to this direction with the proliferation of Titans, ships so large that their gravitational pull can mess with the tides of the planet they're orbiting. The current count for Titans owned by players is measured in hundreds, and the NPC empires are implied to have even more.
Homeworld actually manages to incorporate the Lensman-like game mechanics directly into its plot (and incidentally, the game is heavily inspired by the Lensman books).
in Star Control the Spathi backstory is that they were peaceful primitive people when some new predator showed up and started eating them, in an attempt to deal with the new threat they progressed from stone tools to atomic technology in less then a 100 years...
In Master Of Orion II the player starts out with electronics, nukes, titanium armor, and lasers. By the endgame, they will be messing around with mining shafts that reach into a planets core, electron-state computing, artificial planets, neutronium, phasing cloaks, and low-level time travel.
At the start of Sword of the Stars, all races begin with peashooters and lasers that couldn't light up a cigar. By the end, tiny destroyers have been replaced with gargantuan dreadnoughts armed with Wave Motion Guns, and Colony Drop weapons. The randomized tech tree adds excitement to the game.
Space Empires, of course, being a 4X game. You start with wimpy proton cannons, advance through the orchard of Tech Trees, and end up able to commit galactic genocide through scorched earth tactics by turning all your enemies' systems into black holes.
Happening in the M.U.G.E.N community with "Uber-Cheap" characters. We aren't talking about the likes of F1, Omega Tom Hanks, Rare Akuma, Legend Gogeta or A-Bomb here- these guys would die in seconds against an Uber-Cheap. We're talking about things like Chuck Norris (obviously), Oni-Miko-Zero (an edit of Reimu who KILLS the opponent before the battle starts), various modifications of Orochi from The King of Fighters series, and other such chars that cause seizure with their flashy, deadly moves. If any of these are defeated, expect their next update to come back with immunity to the move that killed it.
Dominions does this with magic rather than technology. The early game typically consists of small scale battles between human armies with medieval weaponry. The endgame typically consists of dredging deadgodsout of Tartarus, arming them to the teeth with ancient magical artifacts, and using them as One Man Armies.
Used as a handwave for the Gun Runners' Arsenal DLC in Fallout New Vegas. When the DLC is installed, the player gets the message that because of the escalating war, the various weapon vendors are bringing out brand new stock, including weaponry, mods and ammo types.
There was also that bit where the author went on about how there are not only missiles and anti-missile-missiles, but also anti-anti-missile-missile-missiles, anti-anti-anti-missile-missile-missile-missiles, and so forth.
Parodied in The Tick. The US military made a sentient mustache because "The Russians were working on a beard!".
Parodied on The Simpsons, where Itchy and Scratchy draw progressively bigger weapons on each other and finally end up with enormous pistols that wrap around the globe.
One of the main causes of World War I. Particularly significant was the naval arms race between all the Great Powers in general and Britain and Germany in particular, which saw the transformation of the battleship from a mixed-gun, smaller vessel to the gigantic, all-big-gun Dreadnaught type, and shortly thereafter increasing numbers of guns, and increases in size, speed, and armor among Dreadnaughts. By the time the War started eight years after HMS Dreadnaught started the trend, the Royal Navy had already commissioned three four-ship classes (the Orion class, the King George V class, and Iron Duke class) of "super-dreadnaughts", all in response to the German campaign to build more and better battleships, which in turn was inspired by the launch of the Dreadnaught in the first place. By the time the Archduke was assassinated in Sarajevo, Britain had 29 battleships, most of them dreadnoughts, with Germany having 17. Ironically, the only time that British and German battleships fought a large battle, it was the Battle of Jutland, a tactical stalemate that can only a be called a strategic victory for Britain by default (the Royal Navy held off the German fleet, maintaining control of the North Sea and the blockade of Germany, but only because two fleets banging futilely into each other tends not to change the status quo).
The irony is actually increased when one examines the actual Battle of Jutland - the Battleships barely engaged each other (the German admiral fled when he realized how badly the British outnumbered him), and instead the smaller and less well armored battlecruisers did most of the fighting that day.
The Cold War, Trope Codifier of the Arms Race in Real Life, saw a constant stream of increasingly expensive military projects pursued by both the United States and the Soviet Union driven by limited or inaccurate intelligence about the other side's plans or Awesome, but Impractical stuff that didn't make it off the drawing board. Essentially, the Cold War ended with piles of technological and electronic innovation because one side went broke from the competition.
A quintessential example: The Soviets caught wind the American XB-70 Valkyrie in the late 50s; it's a long-range, super-fast bomber intended to scream overhead and have landed before its bombs do. By 1970, they had created the MiG-25 "Foxbat" interceptor to catch it. The Foxbat is a brick with engines, and needs huge wings to keep it from falling from the sky, but Yanks With Tanks saw those huge wings and thought, "Oh-crap, an ultra-maneuverable superfighter!" They spent a fortune developing the F-14 (1974) and F-15 ('76) to beat it. This caused the Reds With Rockets to counter with the Su-27 ('84) and MiG-29 ('83), which caused America to field the F-22 Raptor (2005) and F-35 Lightning II (????). The Russians With Rusting Rockets are scrambling to produce their own fifth-generation fighters, but they are hampered by budget constraints, and so America currently has the edge and can now safely operate the XB-70 Valkyrie. ...Or could, if it hadn't been cancelled. In 1961. Before its first flight.
Or the B-2 Spirit stealth bomber, which was built to hunt down Soviet SS-24 and SS-25 mobile ICBMs, which were built to hide from US "counterforce" ICBMs like the MX and Trident that were intended to survive a first-strike and still be able to destroy the other side's missiles, which were designed because the US believed that the Soviet SS-18 ICBs could do the same thing, and so on.
A peaceful example from the Cold War is the Space Race. The Soviets put a satellite into orbit and get a man into space and back in one piece, so the Americans ramp up their space program and eventually get men onto the moon.
At the opening of World War II, the Royal Navy and the US Navy was still deploying biplanes.note in a famous instance, very effectively because they were so slow they could not be targeted accurately by a battleship's flak batteries. By the end of the war, the Nazis were fielding jet fighter planes and ballistic missiles (the Royal Air Force also had jet fighters, but neither side's jets ever fought the other's). It ended with the United States Curb Stomping with two atomic bombs.
Similar tactics were seen in localized areas - for example, the Russians built the T-34 to stop the Panzer, so the Germans built the Panther and Tiger tanks to beat it. The British had already developed night carrier techniques (no one else bothered, which the USN was very thankful for at Pearl Harbor), and once it all kicked off, everyone else scrambled to do the same. When they realized that the Brits fitted armored decks to their aircraft carriers (which made the usual reaction to a Kamikaze attack: "sweepers, man your brooms"), the Japanese built the MXY 7Ohka, essentially a manned cruise missile, to stop them. When it became apparrent that Tiger and Bengal Tiger tanks vastly outclasses Shermans, the USA simply built lots more Shermans and Zerg Rush-ed them.
The Shermans were a bit of a subversion. Improved designs were made, such as the Sherman Firefly, fitted with BFGs, and a much heavier tank, the M-26 Pershing, but there were concerns that halting production of the Shermans to retool for mass producing the more powerful tanks, as well as having to complicate the American's 3,000 mile long supply chain with new parts and ammo for the new vehicles, could actually cause the balance to shift in favor of the Germans.
The Germans invented ever more complex systems of radio guidance for their bombers
Only to have the British deploy even more complex counter-measures.
Now that the pseudo-Alliance the two had during the Cold War is officially over and China is trying to bring itself to modernity, it is beginning to develop a military with which it can actually defend itself properly - which it basically couldn't, until this last decade or so. Currently, the USA has a fixation on China's new stealth fighter prototype, the Chengdu J-20, while the United States' F-22 is semi-grounded for oxygen problems they can't seem to pin down or fix and the F-35 is suffering from both technical and funding issues. In March 2012 a video was taken of the J-20 showing various tests done in flight, this is expected to be used in the ongoing F-35 funding wars to justify its enormous expense.
In 2010, Japan built a life-sized, 60 foot tall statue of the title Gundam robot from Mobile Suit Gundam. In 2011, the People's Republic of China countered by building their own60 foot tall robot statue, which is a shameless rip-off of the Gundam (which they don't have the copyrights or permission to build) except that it is painted orange.
In the automotive world, look no further than The Canadian-American Challenge Cup, or Can-Am for short. An odd racing series, Can-Am had very few restrictions for cars: if it had an engine and was covered in an enclosed body, it was approved. Soon, companies started to make their cars more and more powerful, leading a race to absolutely absurd heights—by the end of the series, Can-Am cars were going Up to Elevenat each successive race having crazy amounts of technology, from fans to increase downforce to six-wheeled cars, and regularly having more than 900 horsepower. Sadly, the series only lasted about a single decade, because the cars were getting too expensive to make and Porsche was kicking everyone else's asses with their 1500-horsepower "Turbopanzer" 917/30KL. Even so, it still was one of the most ridiculous and over-the-top racing series ever.
Along more tragic lines, the Group B rally series of the 1980s was based around a relaxed set of homolgation rules, freeing manufacturers from the requirement to build their rally cars with one eye on commercial mass-production. The cars quickly transformed from rear-wheel-drive models powered with 200 bph engines into four-wheel-drive monsters with 400 bhp turbo-supercharged engines stuffed into kevlar bodies that only vaguely resembled the family hatchbacks they were based on. The series developed a dangerous reputation, and in 1985 driver Attilio Bettega was killed during the mountainous Tour de Corse, when his car left the road and hit a tree. Things finally came to a head in 1986; in March, Joaquim Santos crashed into a wall of spectators, killing three, and in May Henri Toivonen and his co-driver were burned to death when their car plunged off the road and caught fire, also during the Tour de Corse. Group B was immediately cancelled.
Various technology duopolies wage their arms race over consumer dollars. Intel vs. AMD, ATI vs. Nvidia, PlayStation vs. Xbox. What's makes matters worse is that brand new technologies restart the race from scratch. Remember when dual processors or physics engines were new?
Adherents of economic competition (e.g. libertarians and Social Darwinists) invoke this historical pattern to argue why competition forces people into innovation.