In an ad for a Snickers commercial, two opposing medieval armies are rushing at each other with the obvious intent to fight. Right when they are about to collide, they stop when they see a guy with modern clothes standing in the middle of them. He then proceeds to get them to agree that they're not really angry, but hungry.
This happened to the title characters in an episode of the 1960s The Amazing Three anime.
The Three Ships Alliance does this to the Earth and ZAFT armies in Gundam SEED, but it soon devolves into a Mêlée à Trois.
They try to do the same thing in Gundam SEED Destiny, too, and mostly fail (until the final episodes).
In Escaflowne, as Van's Humongous Mecha is getting Curb Stomped by the Phlebotium-enhanced leopard twins, Merle runs out and interposes her tiny little self in front of him. The twins back off from delivering the killing stroke because she's a catgirl like them.
Ash tries this in Pokémon: The First Movie. It does stop the battle, though he probably should have waited until after the Beam-O-War had ended before running in. He dies. Momentarily.
Gunslinger Girl. After the terrorist Big Bad has been captured, the Italian government decides the Social Welfare Agency has outlived its usefulness and sends in the army to destroy them. Cyborg girl Claes however takes the guns off the SWA personal, walks out to the armoured personnel carriers facing the compound and calls on them not to fire. The soldiers are reluctant to shoot a little girl, so the SWA is able to surrender peacefully. The act is particularly significant as the cyborg girls were created to take advantage of the Wouldn't Hurt a Child trope to kill their enemies.
Happened at the climax of Alan Moore's D.R. & Quinch Get Drafted with the entire gang caught between the enemy Ghoyogian Army and their own Space Marines platoon with whom they're in trouble for creating a friendly fire incident with a tactical nuke. Waldo attempts one plea for sanity by stepping up to "cry out at the horror and injustice of war..." It doesn't work.
Performed by Rogue a number of times, for instance she stood between Magneto and a group of trigger-happy soldiers on two occasions with the same issue-number (in both cases she was not bullet-proof), first in Uncanny X-Men #274 in the Savage Land with a S.H.I.E.L.D. and Russian squad and later in X-Men Legacy #274 in Washington, D.C., with a group of U. S. soldiers and police.
Star Wars Downunder. After killing the evil Darth Drongo who has been hoarding all the beer on the planet, Jedi Knight Merve Bushwacker emerges from his base brandishing a beer can, and calls on Drongo's mooks and the rebel forces to stop fighting.
Merve: Look! Look at it! It's cold! It's frosty! It's beautiful! And you're all about to kill each other for it! Stop this madness now, ya boofheads! There is enough for everyone!
At the climax of Ace Ventura: When Nature Calls, Ace stops two mounting armies by running between them holding the sacred bat they had been about to fight over.
He was also yelling said bat's sacred name (which everyone instantly bows to upon hearing it earlier in the film) at the top of his lungs for maximum effect.
In Son Of Godzilla, the titular son and the little kids that befriended it simultaneously stand between the furious Godzilla and the armies amassed to fight the beast.
Mr Pink gets between Mr Blonde and Mr White, who are approaching each other with murderous intent, in Reservoir Dogs.
Near the beginning of The Malloreon, the sequel-series to David Eddings' The Belgariad, Belgarion pulls this, mostly to demonstrate how much he's grown up since the previous series. He stops a civil war in Mimbre by basically riding out between the two armies, unhorsing everyone who gets in his way, and then calling down a cataclysmic thunderstorm between them, while suggesting that anyone who wants to start fighting, can start by fighting HIM. Considering how eager Mimbrates are to go to war, nothing less would have done the trick, probably.
In The Hobbit, Gandalf stood between the Three Armies (Human, Elf, and Dwarf) to point out their common enemies the Goblins were approaching on Warg-Back.
In Men at Arms, Carrot had a truly epic example when he successfully shamed two armies of trolls and dwarves. They were ready to rip each other apart until he came and basically told them that their dear old mothers would not be proud.
Brutha in Small Gods arrives alone on the beach where the armies of half a continent are expecting to fight the Omnian Divine Legion, and explains that the reasons for the war have gone. Almost subverted when one of the enemy generals explains, not unkindly, that sometimes there's just going to be a war and there's nothing anyone can do about it, certainly not by invoking "reasons" or lack thereof. Luckily Brutha has more persuasive allies.
Ronnie from The Last Song stood between Marcus and Scott to stop them from fighting.
The first Ring of Fire anthology contains a story entitled Between the Armies which is this trope grown to a europe-wide scale. It features Jules Mazarin, see Real Life, below.
Live Action TV
In Star Trek: Enterprise, Trip (currently commanding the Enterprise, as Archer and T'Pol are on the surface) stops the Vulcan and Andorian ships from firing on each other by targeting both sides, and saying that he will fire on whoever shoots first.
Buffy does this once with Angel and Riley in Buffy the Vampire Slayer , saying she'd put them (well, Riley, since Angel is a vampire) in the hospital if they kept arguing and wanting to get physical.
Romeo does this to Tybalt and Mercutio in Romeo and Juliet, but things go awry when his interference results in Mercutio getting fatally wounded:
Why the devil came you between us? I was hurt under your arm.
From Fire Emblem 10: Elincia tries to prevent the Begnion Army and the Laguz Alliance from fighting. It succeeds as far as averting the battle by convincing the generals of both sides to back off, but then Senator Valtome of Begnion gets so mad that she thwarted the battle that he sends his own personal troops for her head.
Guild Wars has this, at the end of the Gyala Hatchery mission.
In Knights of the Old Republic, if your Player Character chooses to spare Freyyr and give him Bacca's Blade, the party will enter the Chieftain's Hall to find Chuundar standing with his Czerka allies on one side, Freyyr and some Wookiee loyalists on the other, and Zaalbar trying to keep his brother and father from killing one another. You can't prevent the inevitable brawl, though trying will net you some light side points, but you can tip the balance in favor of one of the factions.
Obi-Wan, Luminara Unduli and her apprentice attempt that in Star Wars Expanded Universe. The armies attack THEM instead, but they somehow manage to destroy all their weapons without killing anyone. Must be the Force.
During Miyako's storyline in Maji De Watashi Ni Koi Shinasai, in order to atone for having let things get so far out of hand while Cap was away, Yamato stops a four-way fight between Wanko, Miyako, Mayucchi, and Chris - with his body. Mayucchi reacts fast enough to pull back at the last moment, but between the other three, Yamato is very much Not OK.
In The Order of the Stick, Hinjo stands between Miko and Belkar just before she can kill him. Only two characters and not two armies, but the lines are awesome:
Miko: You would stand between me and this murderer?
Hinjo: I'll stand between any two murderers I wish.
In a South Park episode, Jimmy and Timmy get the Bloods and Krips together for a lock-in in the gym, then stand between them while Jimmy gives a speech. It works about as well as you'd expect such a thing to work in real life. Don't worry, just like Jimmy told you, a gym lock-in always works.
In most other episodes, it doesn't work that well.
In The Problem Solverz episode "Breakfast Warz", the titular trio does this when Danny's mom and Professor Sugar Fish begin fighting. Horace then gives a speech about compromise, with "Pomp and Circumstance" playing in the background.
The almost-battle of Casal, October 26, 1630. The Spanish and French armies (about 50 thousand soldiers put together) had already begun to exchange cannon fire when Vatican diplomat Jules Mazarin rode out between them declaring that peace had been made.