Naruto featured Ninjas vs. Zombies Ninjas. Yeah, ZOMBIE ninjas.
Due to its Fantasy Kitchen Sink nature, Mahou Sensei Negima! has had Ninja vs. Mage, Mage vs. Demon, Mage vs. Samurai, Mage vs. Vampire, Vampire vs. Samurai, Vampire vs. Martial Artist, Vampire vs. Demon, Mage vs. Swordsman... well, you get the idea. And then the time travel, teleportation, petrification, plant control, and summoning come into play...
The culmination of one of neg's master plans was to have normals donning magic gear and fighting against robots. That's Mage Army vs Robot Army!
Grenadier: it opens with samurai vs. riflemen, and just the first episode also includes riflemen and machine guns against one six-shot revolver plus Improbable Aiming Skills. It goes from there: revolver vs. magical weapon, revolver vs. super-weapon, revolver vs. magical lance, ...
Pokémon often gets by with this, especially whenever the Olympus Mons make the scene. The movies in particular are all about showcasing massive battles between some of the most powerful creatures from the games, whatever the rest of the plot might be about. The newest one makes a point off advertising that the original legendary Mewtwo shows up to face the latest, Genesect.
There's a mini-arc of Gold Digger in which a princess and her spec ops team pilot an ersatzVoltron against a group of pirates and their GaoGaiGar lookalike. The fight lasts three issues and includes triple-wielded katanas, evil twins, and a guitar riff that can stop time. Did I mention that all of the characters involved are leprechauns?
Deadpool tended towards this for a while, especially after he teamed up with his own zombie-universe severed head to fight dinosaurs, some of which became zombies, and then later were infected by the Venom symbiote. He also helped a superhero trucker fight alien raccoons, and helped Hercules solve a labyrinth created by Arcade, who was hired by a demon.
Forever Evil: Lex Luthor's Legion of Doom against the Crime Syndicate.
One Star Wars comic has Boba Fett versus Darth Vader. It's precisely as badass as it sounds.
Dungeon Keeper Ami features a sizeable undead fleet in the opening stages of the battle of Dreadfog Island. Flying undead galleons and frigats, supported by twelve ancient death priests, pitted against airships. And then a giant flying zombie Octopus...
The Godzilla franchise mostly deals with the titled mutant dinosaur himself fighting off other giant monsters and super weapons such as other giant mutant dinosaurs, bugs, dragons, gods, space monster, robots and cyborgs.
There's also the sequels Mega Shark Vs. Crocosaurus and Mega Shark Vs. Mecha Shark, as well as the unrelated Mega Python Vs. Gatoroid. Apparently, The Asylum has a thing for creature features when they're not busy ripping off currently popular movies.
Lucio Fulci's Zombi 2 features the ultimate underwater battle... zombie versus shark! The undeath-or-death duel ends in a draw: the zombie's missing an arm, but the wounded tiger shark swims away, where he presumably goes Up to Eleven by becoming an offscreen zombie shark.
Pathfinder: Native Americans vs. Vikings. Bonus points for having actually happened in Real Life — the Vikings reached America almost five hundred years before Columbus, and even tried to colonize Newfoundland, but were driven out by the natives.
A hundred points to wizard Harry Dresden, for riding out on the back of a zombie T-Rex to face off against necromancers and their zombie armies at the climax of Dead Beat. Plus several million for riding out on said T-Rex to the jaunty tune of polka. Harry Dresden uses a loophole in the series' rules against using necromancy. The Fifth Law of Magic prohibits raising the dead, but as Harry points out (to two people who could legally cut off his head for breaking said Law): "That only applies to raising HUMAN dead." The specific skeleton is, in fact, Sue, aka the most complete T-rex skeleton so far found. Minus one point since fossilized bones aren't, technically, bone, and thus shouldn't be reanimate-able.
Dead Beat features ninja ghoul versus valkyrie security consultant.
"Sticks and stones may break your bones, but Chinese throwing stars get you a dozen stitches."
Changes has an epic battle. Involves three vampires, The Fair Folk, a Knight of the Cross or three, dozens of wizards (including the new Winter Knight and the Blackstaff), a Chinese guardian spirit, an entire army of Japanese kenku ninja-spirits, and Odin versus the entire Red Court of vampires, including the Red King, armies of half-vampire acolytes, and the Lords of the Outer Night, more or less Mayincatec gods, and South American mercenaries.
Santa Clause and the Erkling versus Cthulhu's buddies.
Everworld; not only do you have gods from various mythologies versus each other, but you also have: Vikings vs Aztecs, Vikings vs medieval knights (plus Merlin himself), Ancient Greek gods vs insect-aliens, etc.
Although they did skirt the obvious by having the pirate fight a knight and the ninja fight a Spartan, likely to avoid trolling.
The guy who programs the simulations actually said that they were avoiding it because no one would agree on the right way to test it, and no one on the losing side would accept the result anyway.
A similar concept was used a couple of times on the teen show, Dude, What Would Happen?, albeit with cheap prop duels rather than computer simulations. Once they even did "Vikings vs. Pirates", meaning northmen pirates against caribbean pirates.
Top Gear delights in pitting one Cool Car against another, but it has also featured Cool Car v. Cool Boat (Ferrari Daytona v. a brand new carbon-fiber superboat) and Cool Car v. Cool Plane (Bugatti Veyron v. RAF Eurofighter Typhoon. And perhaps the ultimate: Cool Car vs. Cool Bike vs. Cool Train. And all of them 60 year old designs.
Professional Wrestling in general is built around this trope, combining sport rivarlies with various gimmicks, from superheroes to deliquents to supernatural characters to utterly crazy people, sometimes mixed with various additional rules, be it Mêlée à Trois, fight in a cage or lumberjack match.
The Shield vs The Wyatt Family at Elimination Chamber 2014 and week later on RAW - both insances had the crowds literally chanting "THIS IS AWESOME!".
The original Dungeon Master's Guide included rules for running crossover battles between D&D heroes and characters from other early TSR games, including Boot Hill (Wild West gunslingers) and Gamma World (post-apocalyptic mutants).
Feng Shui features this a lot, given its timehopping Secret War setting. Shaolin monks battle evil cyborg demons from the future, transformed animals fight evil sorcerers that can turn them back into their regular animal form, maverick cops and heroic triad gangsters fight intelligent cyborg apes and their minions who like to BLOW THINGS UP. And that's just for starters.
As one person said, "Exalted is robots versus dinosaurs!" More aptly, it's glorious golden demigods and keepers of the earth, shapeshifting social engineers, a magically-empowered martial dynastic empire and fate's ninjas versus the undead servants of oblivion, mad fairies from beyond reality, demon-kings who gain power from acting like B-movie villains, Communist cyborg soldiers from another dimension, and each other.
Smash-Up is built on this trope. Players choose two "factions" from eight - including Pirates, Ninjas, Dinosaurs, Wizards, Robots, Zombies, Aliens, and Tricksters - shuffle those two factions together, and compete with the other factions to destroy buildings and landmarks. Get ready for Dinosaurs and Ninjas versus Aliens and Pirates!
When you get tier 3, you can start to pump out really awesome stuff like dual barreled tanks with rocket launchers, alien tripods with EMP and triple lasers and stealth robots armed with dual lasers and flamethrowers.
The Allies, a United Nations expy with shotgun-toting riot-police troopers, machine-gun armed hovercraft, huge fleets of bombers and attack aircraft, battleships that can turn to mobile land-fortresses, gunships armed with freeze-rays, trained attack-dolphins, and more.
The Soviet Union, with longcoat-suited conscripts, armoured war bears, heavy troopers with lightning guns, armoured juggernauts the size of houses, zeppelin bombers, and molotov-cocktail-throwing biker troops.
The Empire of the Rising Sun, with samurai foot-soldiers with laser-katanas, ninjas, hyperactive teenage girls in flying rocket suits, a girl with psychic powers, and more mecha than you can shake a stick at.
Assassin's Creed I's plot line revolves around the rivalry between the Knights Templar and the Hashashin.
Scribblenauts allows you to pit nearly everything that's cool against nearly everything that's awesome.
Guilty Gear and BlazBlue. The former has pirates (in a raincoat or sailor-fuku), police (that're dressed in something like priest clothes), assassins, an American Ninja and a whole lot more. The latter has what is essentially the Joker as a Smooth Criminal, cat-people, cyborgs, vampires, a Mad Scientist, and more.
Kongai, a superbly balanced online card game about battles involving Samurai, Ninja, Vampires, a Barbarian Tribe, Pirates, Knights, Robots and Witches.
The player can become a vampire or werewolf, and you fight dragons. There's also ninja assassins, wizards, demons, shadowy goblin-like elves, evil Nazi elves, and giant dwarven robots. You can even fight mammoths, saber-toothed cats, and giants!
Super Smash Bros. Brawl finally lets fans of the "16-bit" generation of consoles pit Mario and Sonic against each other.
Mass Effect combines the three Super Smash Bros examples above, and the plot centers around alien vs. robot fights. One of the coolest in-game combinations comes in 3, where the heroes summon a gigantic Thresher Maw (that is, gigantic by Thresher Maw standards) to fight a Reaper. The Thresher Maw wins.
3 also has references to a Reaper-aligned infantry vs. krogan cavalry battle. To elaborate: the Reaper infantry are murderous cyborg zombies who make the Borg of Star Trek seem gentle. Krogans are one of the most badass races in the galaxy, capable of enduring virtually any kind of punishment and surviving, whose idea of a coming of age ritual involves fighting their planet's most brutal wildlife, up to and including going five minutes in the ring with a Thresher Maw. Also, for this battle, they are riding cloned dinosaurs. That sound you just heard was your soul exploding from pure awesome.
Touhou: Take your pick: Miko versus Vampires, Ninja Maid versus half-ghost samurai gardener, vaguely-lesbian Witches versus Immortal Aliens, Dumbass Fairy versus The Judge of The Dead, Shrine Maiden versus Gods, Witch allied with Mad Scientist versus Nuclear-powered Raven from Hell, Holy Frog vs. Celestial Paragon, Treasure Hunters vs. magical Dr. King, Witch vs. Liches, literal Cloud vs. sentient Noh Masks, Paparazzi versus everyone... explained by Gensoukyou being the last refuge for fantasy.
One of the main attractions of the Total War series, especially Rome, Medieval and Empire. In a historical-based Real Time Strategy game, irregular wars that never historically happened do break out with alarming frequency. Spanish conquistadors holding the line against Mongolian horse-archer raiders? That can happen. The Independence-era United States attempting to conquer, or being conquered by, the peoples of the Indian subcontinent? Can happen. Viking warriors invading Aztec Mesoamerica? Possible. Carthage conquering Rome and moving north to fight the Celts? Plausible. Scottish highlanders storming Cairo? ... Has been done already, but the point still stands.
The popular Medieval II mod Thera is a bigger example of this, as it adds a number of Fantasy Counterpart Cultures to a Low Fantasy setting. Celts? Pirates? Samurai? Orcs? Medieval Transylvania? One gets the feeling the mod was pretty much designed with this trope in mind.
The Mount & Blade series shares much of the same appeal as mentioned in the Total War entry above, and while it's watered down a little since they're from Fantasy Counterpart Cultures, that's mitigated by the fact that the player can actively fight alongside them. Want to lead hordes of deadly steppe-raised horse archers against Viking-esque Sea Raiders (or vice-versa)? It's doable.
In Bioshock Infinite, both the Founders as the Vox Populi make heavy use of Motorized Patriots, basically the 1912 variant of the Terminator, as Elite Mooks. There are times when you can summon one of the Founders to counter those of the Vox Populi, resulting in a giant motorized Abraham Lincoln (the Vox) and George Washington (the Founders) duking it out in the streets, spouting lines as "Blood... is the price... for liberty!" or "The Lord judges. I act." while emptying their miniguns at each other.
Age of Mythology throws Classical Mythology, Egyptian Mythology and Norse Mythology into a Mêlée à Trois. Armies of Greek hoplites backed up by centaurs and minotaur heavies, up against Egyptian footsoldiers with sphinxes, mummies and giant scarab beetles, taking on Viking warriors fighting alongside trolls, valkyries and wolves. The expansion adds Atlantis as a civilization, and the Titans; massive super-units capable of devastating whole armies single-handedly note The Greeks get the three-headed dog Cerberus, the Egyptians get the god of vengeance Horus, the Norse get the gigantic frost giant Ymir, and the Atlanteans get Chthonian, a lava giant covered by crystals spikes sprouting from various parts of its body..
The Adventures of Dr. McNinja has had, in no particular order, ninjas and a doctor ninja versus... robots, clowns, a flying bodybuilder, a giant Paul Bunyan who was really a child, evil ninjas, pirates, ghosts, Mexican banditos on dinosaurs, vampires, zombies, a unicorn motorcycle, a ghost wizard, someone pretending to be a robot, ninja zombies, more robots, zombie Benjamin Franklin, Dracula (Dracula also had a robot Dracula), a Danish 80s action movie hero and his ninjas, clone ninjas, ghost wizards, Mayincatec robot temple guards, future dinosaurs from space, a vengeful space ghost that explodes people, a samurai demon, sky pirates, a luchador doctor, and a king on a dirtbike. At any given point, those enemies may have fought each other as well.
Axe Cop has had the title character and his allies (including dinosaurs, people with unicorn horns, a vampire wizard ninja and his brother who's also a werewolf) vs. aliens, vampire half-babies, Humongous Mecha, flying books, Bad Santa... This picture◊ with just about all the good guys and antagonists on opposing sides, with huge amounts of Ninja Pirate Zombie Robot in both, takes the trope about as far as is imaginable.
Ethan Nicolle's other webcomic (besides Axe Cop), Bearmageddon, opens up with a character asking another who would win in a fight, a bear or a gorilla. They decide that it's an unanswerable question, like "can God make a square circle".
The Dragon Doctors is about magical doctors of many different disciplines who have banded together, and they've fought against various equally unusual opponents. The docs themselves are a wizard (with healing and shapeshifting magic), a soldier/surgeon, a shaman/therapist, and a Magitek specialist. They've faced off against a horde of assassins, a serial killer who kills dreaming shamans, and Goro (the soldier/surgeon) is currently fending off an all-female Quirky Miniboss Squad consisting of a pistol-wielding shapeshifter, a mage in a ballcap, a female ogre and a lamia with a petrifying ray gun.
Narbonic: "Who would win in a fight between a giant robot foot accompanied by a rifle-toting assassin, and an army of hamsters in mechanical suits?"
Homestuck has Bro (a Crazy Awesome, katana-wielding Badass who flies around on a rocket-powered surfboard) versus Jack Noir (a noir-themed Humanoid Abomination with godlike powers who also wields a katana and is part dog). The resulting battle is so awesome that it ends in a tie, with the two fighting to a standstill. Jack later gets the upper hand and kills Bro but only thanks to a well timed power-up gained from Becquerel prototyping himself.
Older Than Feudalism: The Battle of Zama. A climactic battle between two of the mightiest empires in history commanded by the two greatest generals of the Sword And Sandal era. On the Carthaginian side is the Magnetic Hero, Hannibal Barca. On the Roman side is the Cincinnatus type Scipio Africanus. Who will win? Rome. To put the Battle of Zama into perspective, you have Roman legions being led by an eccentric general who really should not have this position under normal circumstances versus the aforementioned Magnetic Hero leading a diverse mercenary army and War Elephants. By all accounts it was epic.
The Battle Of Leuctra: The Theban Sacred Band versus The Spartans. The Thebans won.
Tennis rivalries - and sports rivalries in general - pretty much run on this trope. Federer vs. Nadal in the present and Sampras vs. Agassi in the past are examples. The 2007 and 2008 Wimbledon Men Singles Championship matches were noted for featuring the two players in their prime fighting tooth and nail for every point.