A very common trope in Anime and Speculative Fiction. One opponent sends out a beam of destructive energy intent on frying their opponent, and said opponent does the same. These two beams slam against each other in the middle, and begin "pushing" back and forth, essentially becoming an energy arm-wrestle. Either one consumes the other and goes on to greet the enemy, one opponent collapses from the effort involved, or else they both explode.
When more than two opponents are involved, they usually join their beam attack with their respective ally (or give them more energy) so that the "intersection" get closer to the opponent. They almost never think about sneaking behind their defenseless foe and beaming them (or just slicing their throat) In the Back.
A slight variation of this trope will have one character creating a "shield", attempting to hold it up as long as they can, lest their opponent's beam of death destroy them.
This has little justification in real-life science. Lasers, for example, will simply pass through each other unimpeded, although their point of intersection may experience any constructive or destructive interference between the two beams depending on the characteristics (wavelength and phase) of the lasers involved. Of course, energy beams in fantasy and sci-fi are up for grabs in terms of how they react to one another, but even then there's the improbability of the beams being fired nearly simultaneously at perfect enough angles to result in a head-on collision with similar enough initial force to force equilibrium without planning such things beforehand. It does work for matter projectiles but those are rarely used.
Beam-o-War is also known as a "power struggle" in certain circles. If a video game has Destructible Projectiles, a variant of this can occur. Compare Air Jousting, Brawler Lock, Blade Lock, and Pummel Duel (the Rapid-Fire Fisticuffs variation of this) for more physical examples. May be preceeded by Blasting Time.
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Anime and Manga
Sailor Moon often fought the Big Bad this way. One battle that stands out was when she fought the Snow Queen in her second movie.
Nearly every major battle in Dragon Ball Z (The Trope Codifier, if not the outright Trope Maker) had at least one of these, the most iconic being Goku and Vegeta's first fight and the arc-ending, episode-long struggle between Gohan and Cell. The movies also feature it, and it's a mechanic in most of the videogames.
Goku vs Frieza: round one, Goku's Kamehameha vs Frieza himself, surrounded by a force-field. Frieza wins by breaking out of the struggle and ramming him. Round two, Frieza pulling a Backstab Backfire after being cut in half by his own technique and saved by donated energy. Goku snaps and finishes him off.
Before the Goku vs Vegeta duel we had Goku's Cho Kamehameha vs Piccolo's unnamed attack. Goku wins.
One happens in Gundam SEED Destiny when Kira and Shinn fire their primary beam cannons at one another.
Mazinger Z: Sometimes Mazinger Z and a Mechanical Beast engaged in this, and usually Kouji used Mazinger's Breast Fire to couterattack their energy beams or waves. Some examples happened in episode 11 and episode 30.
The final battle in season one of A Certain Scientific Railgun ends with one of these. Despite Therestina boasting that her artificial railgun attack was more powerful than the original, Mikoto's railgun overpowered Therestina's for victory. Seems the animators forgot that railguns use physical ammunition, and if this actually happened the result would be a powerful explosion with supersonic shrapnel, not a power struggle.
Spoofed in Excel♥Saga, during the final struggle between Pedro and That Man. During a Beam-O-War struggle, That Man one-ups Pedro by taking one of his shoes off and firing an energy beam from his foot.
In Neon Genesis Evangelion, there is a notable subversion in the battle with the Fifth Angel, Ramiel: both it and Shinji fire energy beams at each other, but the beams don't meet; their energies warp each other when they get close and they both veer off wildly. Shinji's weapon fires a positron beam, implying that the Angel's weapon is similar and the two electrically charged particle streams are therefore repelling each other. Played straight in Evangelion 2.22, though.
Similarly, in Mai-Otome, Natsuki and a gigantic laser battery fire beams at each other, and both are diverted away from their target — but the battery's shot still hits close enough to seriously damage the nearby Macguffin.
In a subversive twist, the title character of Magical Girl Lyrical Nanoha wins a beam-battle against rival Fate, only to lose when the resulting lightshow blinds her to the latter's movements. A smokeless Smoke Shield, as it were. Later on, however, she does win both a "shield versus beam" match and a "beam versus shield" match, one right after the other. This gets played around with several times later in the series. Fate attempts to use the same "use explosion from beam of war to hide movement" trick against Chrono in the A'smanga only to fly right into a delayed Bind spell prepared by the more experienced Chrono. And in the penultimate episode of StrikerS, Vivio used the same trick on Nanoha, except Nanoha was prepared enough to raise a shield against the sneak attack. Unfortunately it still proved useless before her attacker's powered punches. The trope is also played straight, such as the Beam-O-War with Dieci in StrikerS where Nanoha, who has been operating under a Power Limiter for the whole series, shows that she is not left handed after all (well, she actually is, but that's besides the point), and wins effortlessly.
A slight variation in Naruto, when Naruto and Sasuke fly at each other with hand-held forces of destruction, which they smash together. It creates a lightshow more appropriately a "Ball O War", which then expands and envelops them both in a black sphere.
Itachi and Sasuke then do this, but with breathing fire. Itachi wins by using Amaterasu, which burns the other fire.
The video games, like the Dragon Ball ones, frequently have this as a mechanic. This can lead to combinations such as Kakashi's lightning-enhanced chakra strike vs Might Guy's foot.
Mahou Sensei Negima! - Negi's fight against Evangeline in the earlier chapters ends in one. (Well, technically it ends right after one occurs, the actual Beam O War really didn't decide anything.) 150 (or so) chapters down the line, the same happens between Negi and Chao Lingshen, literally deciding the victor of the Battle of Mahora.
Played with in the Negi vs Chao battle. In most other shonen action manga, one would expect the battle to be won by overwhelming power and Heroic Resolve; here it's decided by Negi's superior battle experience. While Chao's spell was more powerful than the one Negi used, Negi's spell had a shorter incantation and covered about two-thirds of the distance between him and Chao before she was able to launch her attack, immediately putting her on the defensive and critically over-straining her artificial magical abilities.)
Negi subverts it again during the fight against Rakan. He tricks his opponent into unleashing an enormous Kamehame Hadoken by putting (supposedly) all of his remaining energy into producing a giant "Titan Slayer" lightning spear and appealing to the opponent's love for contests of strength. Rather than throwing his spear to cancel out the blast, Negi absorbs both his Titan Slayer and Rakan's blast and uses the power boost to beat Rakan into (near-)submission.
An interesting shield vs shield variation happens in Transformers Cybertron between Galvatron and Starscream, where their Battle Auras are extended as an attack and meet. This creates a spectacular lightshow, but is ultimately the warm-up and the battle is decided by Punch Parry instead.
Trigun had one in the final episode, when Knives tries to fire his angel arm at Vash, who responds with his own. While a chunk of perfectly good real estate is turned into a crater and the sky turns that distinctive post-apocalypse red color, the destruction is relatively limited and both Vash and Knives are unharmed, suggesting that their weapons largely nullified each other.
Pokémon had a few of them. Notably an Ice Beam/Night Shade collision at the Orange League final, which exploded in a Yin-Yang esque light ball and knocked out both Pokemon. Or, for that matter, some kind of variation every single time two Pokemon attack at the same time in the new series. And they always make the exact same explosion. Even if it's LEAVES AND WATER.
Seen in one Yakitate!! Japan opening between Azuma and the Kayser brothers, but never actually done in the anime, thankfully.
The Big O, between the Big O and Big Duo in episode 12.
Tengen Toppa Gurren Lagann, in its duel between Simon and Nia in the Lagann and Lordgenome in his Lazengann, features a variant on this that can only be called a Drill-O-War. No beams involved, but every other factor was classic Power Struggle.
In Lagann-hen, another Drill-O-War happens, this time beyond their typical fashion. Super Tengen Toppa Gurren Lagann unleashes its universe-sized Giga Drill Break, and the Anti-Spiral follows with its own Giga Drill Break. In other words, [[spoiler: the Spiral Nemesis (or at least some form of it, as the Spiral Nemesis explanation was very specific), what the Anti-Spiral was trying to prevent, happens. The universe starts to collapse in on itself as the two drills spin against each other. Good thing it was the Anti-Spiral's pocket universe, with no other life-forms (hopefully, after all they were throwing galaxies around like shuriken), or else everyone would've been dead.
Occurs several times in Code Geass, all in the second season (at which point each side had acquired beams with which to war).
Used in the fifth episode of Tenchi Muyo! during the fight between Ryo-Ohki/Ryu-Oh and the Souja. The Souja wins.
During Ranma 1/2s duel between Ranma and Ryouga in which the former canceled out the latter's depression-fueled Shishi Hokodan with his own arrogance-powered Mouko Takabisha. But then Ryouga, depressed further by his attack being countered, delivered an even bigger Shishi Hokodan that popped Ranma's Mouko Takabisha like a soap bubble.
Tsuna and Xanxus of Katekyo Hitman Reborn! in the Sky battle. One shoots them from his guns and the other from gloves. It was pretty much Tsuna's only defense and attack then.
So far Digimon Xros Wars has had this twice, once with Shoutmon X4 vs. DeathMeramon and another vs. AncientVolcanomon. The first time, Shoutmon X4 fired a drill from his shoulder at DeathMeramon's feet as a distraction. The second time, AncientVolcanomon fired another Big Bang Fire on top of the first for an extra push.
It also happened a few times in Medabots, most of them involving Metabee when he taps into the Medaforce.
Actually invoked at the end of YuYu Hakusho's Dark Tournament arc, when Toguro proposes he and Yusuke skip what would doubtless be a protracted battle, drop all their limiters and put everything into one blast, winner take all.
In Senki Zesshou Symphogear Episode 11, Chris uses her swan song to essentially go strike freedom on an Ion Cannon named Kadangir, which is supposed to be strong enough to destroy the moon with one blast. She fails, but she manages to weaken the blast enough to only have a chunk of the moon be blown off at the cost of her life.
In one of the Inuyasha movies, a baddie copies Miroku's Wind Tunnel and they duel....somehow. You'd think they'd instantly suck each other up or something.
Havok and Cyclops of X-Men can do this, but there's very little point. Since they're brothers with powers that operate similarly, they simply absorb and metabolize each other's blasts.
The second season finale of the animated series culminates in a Beam-O-War between Cyclops and Mister Sinister, with a laser pistol-wielding Morph as the deciding factor.
Havok once engaged in a beam-o-war with his evil counterpart, the Living Pharaoh. It ended with Havok getting sealed in a case that shielded him from cosmic rays (thanks in part to a Spider-Man blunder), resulting in the Living Pharaoh taking all the cosmic rays for himself and transforming into the Living Monolith.
Cyclops tends to do this a lot. In a crossover with the Agents of Atlas he and M-11 got into a Beam-O-War. Since they both shoot beams out of their eye(s) Iceman called it a staring contest.
In the Agents' first ongoing, M-11 had a Beam-O-War with the more powerful M-21 - and lost, getting blown to kingdom come (it's okay, he got better).
In the original Squadron Supreme mini-series, Hyperion fought his duplicate this way, each using their atomic vision.
The battle was so intense that even though the evil Hyperion got hit with all the accumulated energy, the good Hyperion damaged his own invulnerable eyeballs to the point of blindness just from the exertion, and Hype is basically Superman.
There exists a comic crossover of Superman and Goku, where there is one of these between the former's heat vision and the latter's Kame Hame Ha. Except Supes wasn't really trying to push back the attack, he was piercing it to get close and punch Goku.
In the Tamers Forever Series there is a brief Beam Struggle between Armmagedemon's Ultimate Flare technique and Seraphimon/Magnadramon's Dual Force: Golden Absolution technique.
Atlas Strongest Tournament: When the changeling plot is exposed and leads to a big battle, we get two examples of this: Amber Spark and the changeling impersonating Rainbow Dash launch their special moves (Jupiter Lance and Sonic Rainboom, respectfully) at each other, causing an explosion when they overwhelm each other. Later on, Twilight and Luna do this jointly with Chrysalis and Aurelia, which ends in a draw.
Chapter Seven of Monsters In Paradise, a Touhou Project/Pokemon crossover, features a showdown between Marisa Kirisame's Magicannon: Final Master Spark and the Terraformation, a superweapon created to purge emotion-heavy life from existence. The Terraformation has the upper hand at first, but Marisa's Mismagius accidentally damages the Terraformation's power supply with an attack of her own, letting the Master Spark overwhelm the superweapon's output and destroy it.
Likewise, there was a Beam-O-War between Lo Pan and Egg Shen in Big Trouble in Little China. Amusingly, instead of having the beams just push each other, a pair of samurai form in the middle of it and fight each other.
Lo Pan: You never could beat me Egg Shen.
Also, during this sequence, Lo Pan is making finger movements that make it look like he's playing a video game.
The movie X-Men: The Last Stand has Iceman and Pyro using beams of ice and fire, respectively. When Pyro starts to gain ground, Iceman abandons the beam strategy and coats himself in ice armor, allow him to just walk over and take down Pyro with an old-fashioned headbutt.
In X2: X-Men United, Jean Grey used the shield variation against Cyclops' eye beams while he is mind-controlled. This is used to show how much stronger Jean Grey is here than she was in the first film.
In Godzilla films, beam fights are common among Kaiju that can fire energy beams. Particularly in the ones with Mecha-Godzilla, which tend to knock both monsters down.
Dark City flies off the rails at the very end, turning into a series of these after running an otherwise very atmospheric Ontological Mystery.
In Star Wars: Revenge of the Sith a variation of this happens twice: Anakin Skywalker and Obi-Wan Kenobi try to Force-push each other, holding each other off momentarily before they're both thrown in opposite directions. During the concurrent Yoda vs. Emperor fight, the Emperor tries shooting lightning at Yoda, who manages to grab it and push it back at Palpatine until the whole thing balls up and explodes, once again sending two combatants in opposite directions.
In the Film of the BookStardust, a brief battle between the witches Ditchwater Sal and the far more powerful Lamia manifests as a Beam-O-War. Lamia's green flames overpower Sal's shadowy magic easily, and go on to disintegrate her head.
In the absolutely horrid 1992 low budget The Fantastic Four movie, the Human Torch does a full-body 'flame on' for the first time near the end of the movie to outrace a laser beam (!) that is arcing from Latveria to New York City (!), and manages to win a beam-of-war with the laser (!) using his flames. Because he always wanted to beat this one video game that had something similar. Oy, vey.
In Iron Man 2, this happens twice between Iron Man and Rhodey. The first was an unexpected side-effect when they got in a fight; the second time it's used to take down Vanko for the last time. This version is a combination of Beam-O-War and Forbidden Chekhov's Gun. This is because the beams in question are thrust streams coming from their flight stabilizers. Unlike lasers, repulsor beams probably actually would "push" on each other violently.
In Dragonball Evolution, Goku and Piccolo get into one for a few seconds. As Piccolo fires his Ki Blast at Goku, Goku fires his Kamehameha wave and flies up at the time giving him the advantage (somehow) and then... KABOOM!
The Harry Potter films use this in the battles between Dumbledore/Harry and Voldemort and occasionally in other duels. It doesn't make any sense in all cases but the first. However, since the films don't explain any of the cases, they all make equal sense in the theater.
This occurs in 1963's The Raven between the characters of Vincent Price and Boris Karloff in a wizard's duel. The graphics of the time were naturally not too great, but at least the beams were color coded.
The climactic scene in Harry Potter and the Goblet of Fire (pictured above) features a magical duel resolved in precisely this manner, due to a rare magical interaction between wands. When Harry "wins", Voldemort's wand is forced to start regurgitating spells he's cast in reverse order. When this reaches his (many) killing curses, it causes shades of his victims to appear, giving Harry moral support and scaring the hell out of their killer.
It also happens in Harry Potter and the Deathly Hallows, except this time the fragments of Voldemort's soul had all been destroyed, including the one held inside Harry's body, which resulted in Voldemort's death when the beams collided.
The Discworld novel Sourcery had two wizards sitting at either end of a long table, discussing the Sourcerer. Both of them want the other one dead, so while they chat, they're preparing nicely explosive spells and throw them at each other at the same time. The spells meet at the center of the table and explode, knocking both wizards away.
In Katherine Kurtz's Deryni novels, there are duels between opposing Deryni in which the energies they fire at each other create half-domes of opposing colors that push against each other. This works a bit like arm-wrestling - the more powerful sorcerer's arc will eventually overtake the other's, incapacitating or killing him. (And yes, the combatants are all men - the setting is based on medieval Europe after all.)
The circle or dome is in fact a containment field erected for the safety of the onlookers. The only time we see control of the circle used as a direct conflict of wills in the duel between Kelson and the Festillic claimant who is a woman. There are plenty of high powered Deryni sorceresses around. Queen Jehana, a previously unknown and untrained Deryni takes on Charissa, the villainess in Deryni Rising. Another Deryni lady fights in defense of her king in 'the Bastard Prince' and Lady Richenda and Princess Morag use their powers in defense of their sons. One of the conventional rules of the Duel Arcane is ceding the first blow to a female opponent. Clearly women duel.
In Robert Jordan's The Wheel of Time Nynaeve's battle with the Forsaken Moghedien consists almost entirely of the two throwing the flows of the One Power at one another at half strength, using the other half to shield themselves from the other's attack. Interestingly the whole thing is invisible to Muggles (or men period) and its noted anyone walking in would have merely seen two women staring at one another. Several other fights have moments of this too. Balefire and the Flame of Tar Valon in particular are described as beams.
The Wizard Duel in The Seven Towers by Patricia C. Wrede, with a subversion: after watching for a while, the protagonist realises that the wizards aren't trying to push each others' beams away, but drag them closer. It's explained afterward that if one wizard succeeds in reeling in the other's beam, he is then able to drain his opponent's power.
In Mercedes Lackey's Joust series, the badguys use magic to concentrate sunlight into what is effectively a giant laser beam. (The official description is that they're focusing and concentrating sunlight at a specific place, but it appears to be a giant beam of white light.) Ancient Egyptian laser beams, indeed. Note that it was built as an anti-invasion device a long time ago and eventually became a tool of oppression and one reason for the gigantic war that ends at the end of the third book. It also ended the war — because it blew up the city it was in, and that city happened to be a national capital housing most of the population, kinda like Mexico City.
Live Action TV
In the Babylon 5 episode "Trust The Corps", a practice telepath attack/defend training session looked like the tentacle + shield variant.
In the Stargate SG-1 episode "The Quest Part 2", Daniel Jackson and Adria have one- Daniel has Merlin's consciousness inside him, and blocks Adria's energy beam attack with one of his own in order to buy the others time to leave through the gate. He loses after the others leave and is taken prisoner by Adria and the Ori.
Seijuu Sentai Gingaman: the battle between the first Monster of the Week, Kolshizer, and Ginga Red's gingabeast, Ginga Lion, featured this kind of fight. The beams in this fight where Kolshizer's lasergun and Ginga Lion's fire breath. Through Gingaman footage, this same battle was also featured in Power Rangers Lost Galaxy, with the monster and the gingabeast being renamed as Radster and Lion Galactabeast respectively.
Power Rangers in Space: episode 18, "True Blue to the Rescue"; Storm Blaster (one of the cars from Power Rangers Turbo) and the Monster of the Week, Lionizer, engage in a Beam-O-War with their lasers. They are evenly matched, untill Justin and TJ tip the scales by adding their own lasers to that of Storm Blaster.
The penultimate episode of Charmed features one of these with the Charmed Ones and their opponents both using The Hollow. Oddly, the Charmed Ones fire six beams while their opponents fire four, yet somehow the beams all still block each other.
MythBusters tested an Internet viral video featuring this between a flamethrower and a CO2 fire extinguisher. Even with a supercharged fire extinguisher, they could not replicate the video (though the supercharged extinguisher did actually manage to stop the flame from reaching Adam).
GURPS: Powers calls this Power Parry and suggests that this only ought to apply for powers that have the same or opposite focus. However it points out that in genres where this is possible in the first place coolness should trump everything.
In the tie-in novel The Brothers' War, a young Urza and Mishra have a Beam-O-War battle between the green magical laser beams of Mishra's Weakstone and the red magical laser beams of Urza's Mightstone. When their mentor Tocasia tries to break it up, the resulting explosion leads to her death.
The game G-Darius actually features this as a gameplay mechanic. Every one of the game's freaky giant robot fish bosses (or "Huge Battleships", in traditional Darius parlance) is armed with a giant beam cannon; luckily, your ship is armed with its own beam cannon, and with good timing and a lot of button-mashing you can turn the Beam-O-War shouting match against the enemy and kill it in one hit.
The presence of autofire in PS1 versions made these infinitely easier as it removes the button mashing aspect. However, later bosses display Dangerously Genre Savvy tendencies, that is, as soon as their Wave Motion Gun fails to yours, they throw WMG-absorbing bullets directly at you, followed by bajillion bullets.
Cyberdrive Zoids also uses this in gameplay - if two beam attacks of similar power collide, it turns into a first-to-100 button-mashing contest to decide whose attack actually hits. Even when the AI gets a headstart, you can usually beat it.
In Boktai whenever you're using the Pile Driver to destroy a vampire's coffin and kill it Deader than Dead, the vampire will try to push back the solar energy beams with beams of dark matter. You can counteract this by shooting the beam generators with your solar gun to boost their power.
All ranged attacks in Little Fighter 2 can cancel each other out or obliterate weaker attacks. Only a few characters have a fast enough rate of fire for an extended Beam o' War, though.
The final battle in Feel the Magic: XY/XX consists of a Beam O' War conflict between the protagonist and his rival, using beams of lightning fired from their mohawks and powered by towels rubbed across the backs of their heads.
In The Force Unleashed, if the player and an enemy both use lightning on each other simultaneously, one of these ensues. If the player can push the right buttons fast enough, his attack goes through; otherwise, the enemy's attack does.
In the final cutscene, Galen Marek and the Emperor do this with Force Lightning, much like the Emperor and Yoda previously had. Also much like Yoda, Marek pushes it back and the resulting explosion sends everyone flying and (presumably) kills the nearby Stormtroopes. The Emperor and Darth Vader are (of course) fine, but Marek himself is supposedly killed by it.
Used in the cinematics of Dead or Alive games: once in the opening to DOA Ultimate between Hayate and Raidou, then again in DOA Dimensions between Kasumi and Raidou. In the former, Raidou overpowers Hayate, and the resulting shockwave sends Hayate flying into a tree and snaps his spine, paralyzing him and putting him in a coma, while in the latter, Kasumi only manages to overpower Raidou thanks to Ryu Hayabusa's intervention.
Godzilla: Unleashed lets two monsters lock beams if they fire them at each other at the same time. The monsters send pulses of energy down the beams (with a flick of the Wiimote) to push the ball toward the opponent. Whoever loses takes the damage of both beams to the face, knocking the monster on its back. However, if the monsters are very close to each other and lock beams, it immediately explodes and sends both monsters flying.
Averted in Magicka where beams hitting head on will explode and obliterate anything within a few feet and cancel the casting of beams.
DoDonPachi DaiFukkatsu has this as an important game mechanic: the enemies frequently fire large quantities of purple lasers which must be blocked by your own laser.
Dogyuun's second boss has a move where it fires out a Wave Motion Gun from its chest, and you can try to counter it with your own Wave Motion Gun if you have the blue weapon. You'll probably lose, though, as he fires out two and you only fire one.
Starcraft II Heart Of The Swarm - Kerrigan and Narud perform one during the Phantoms Of The Void mission. Narud is slowly winning due to being powered up by nearby temples, once they are gone he loses in seconds.
In the episode "Maximal, No More", Dinobot and Quickstrike clash beams in a sparring match (the former's being Eye Beams). Dinobot's beams are initially pushed back, but he wins by simply walking forward and closing the distance between them.
The episode "Double Dinobot" has a similar fight between Megatron's pink-ish arm laser and Dinobot's green Eye Beams. They form a roiling pink-and-green ball that's shoved back and forth. It ends when a missile from Optimus Primal strikes the ball and sends both combatants flying.
And in the final episode, Tigerhawk loses a Beam-O-War against the Decepticon warship Nemesis. The fact that he was even able to fight it is impressive.
Happened in the first episode of Dave the Barbarian when Dave fought the Dark Lord Chuckles the Silly Piggy. Dave even commented on their beams being evenly matched, but Chuckles said it was just because his mystical item was set on low. Once he set it on full power, Dave lost instantly.
In Megas XLR episode paying homage to the whole Mecha-Godzilla idea (see below), Gorrath makes a Glorft version of Megas and the two robots have at it at the end of the episode. Gorrath lets loose eye lasers and Coop responds in kind with lasers from the headlights of his robot's car-head. They are evenly matched until Coop flips on his car's high beams.
Danny and Vlad did this with Ectoplasmic Rays in Danny Phantom, only for Danny to lose when his Opposite-Sex Clone comes up from behind and knocks him unconscious with her own blast.
In The Simpsons episode parodying the death of Dumbledore in the Harry Potter books, the death in question occurs in a much more straightforward fashion than in the books with "Lord Greystache" facing the series' Big Bad in a beam-o-war. Unfortunately, he is forced to break off his attack in order to save the protagonist from a grisly death, rendering him defenseless. Homer invokesFanon Dis Continuity and makes up a new ending on the fly where the duel is resolved in a different manner...
Greystache: MUSTACHE POWER: ACTIVATE!!
The battle between Big Guy and his robot double in Big Guy and Rusty the Boy Robot involves this, it ends when Dwayne his operator fires Big Guy's hand into the double's cannon blowing him up.
Justice League has Superman and AMAZO matching heat vision. AMAZO cheats and uses Green Lantern powers to give himself an edge.
And on JLU, Red Tornado goes up against three Wind Dragon clones simultaneously, performing this trope with cyclones rather than beams. Red Tornado comes out on top, almost embarrassingly easily.
The various DCAU Green Lanterns also have a tendency to get involved in the 'shield' version, on either side.
In Teen Titans, Raven fights against Trigon in this way in "Nevermore".
In Doug, one of Doug's Quailman fantasies involves him fighting a mad scientist version of Roger Klotz who uses a hypnotizing "brain drain" ray. He counters it with his Quail Vision, and they are evenly matched until he turns on his "Quail High Beams" and wins.
That was actually two fantasies, and Quailman lost the one with the brain drain ray. The one where he won was when Dr. Klotzinstein had an ability called the "Eye of Klotz" which could turn people into rodeo clowns.
Downplayed in a Superman cartoon that featured the Man of Steel literally punching the daylights out of a laser beam. A later episode had a closer variation, with a magnetic beam and a comet having a physically improbable shoving match before the comet is finally sent back into space. This later got a visual Shout-Out in Superman: The Animated Series, with Superman using the same laser-punching technique to defeat Brainiac when the latter first invaded Earth.
Used symbolically in the fight between Aang and Ozai, where the beams spewed out of their bodies into the sky, with one's color's dominance in the light show showing how close he was to psychically dominating the other.
The shield variant also appears, with Aang hiding in a ball of rock while Ozai tries to Kill Him With Fire.
Adventure Time: Finn the Human has one of these in a fight with a wand-wielding evil piglet. Finn's beam is a stream of ice cream.
In the final episode of My Little Pony: Friendship Is Magic season two, Princess Celestia tries to defeat Queen Chrysalis of the Changelings by shooting out an arcing beam of magic from her horn. She tries to counter with one of her own and, to even her own surprise, is able to push back and stun Celestia, due to the strength of the love she has been feeding on.
There's also one between Blue Beetle and Black Beetle in "Before The Dawn". The two fire their plasma cannons at each other which results in an explosion that sends them flying back.
In the season 4 finale of Winx Club, the Winx and Nebula, get into one with the remaining Wizards of the Black Circle. The Wizards are outnumbered and low on magic, so it ends with them being frozen in ice.