The Menos Grande and some of the Arrancar do this with their Cero attacks. Nnoitra has a slightly creepy variant: he fires his from the tip of his very long tongue. Ew.
Nelliel has a technique called Cero Doble: she can eat Ceros and then fire them back with the combined force of her own Cero.
Taken further by the Espada Baraggan Louisenbairrn, whose "Respira (Death Breath)" will cause anything it touches to rot into nothingness.
Bubblegum Crisis: Several of the Boomer robots had beam cannons hidden in their mouths.
Di Gi Charat: Piyoko has her Upchuck Bazooka attack to counter the title character's Mekara Beam (which she shoots from her eyes).
Digimon: Rather common for Child/Rookie and Adult/Champion Digimon, but higher evolutions tend to have actual weapons.
Child Agumon and Adult Greymon are fire-breathing dinosaurs, Perfect/Ultimate MetalGreymon is a cyborg with missiles and metal claws , and Ultimate/Mega WarGreymon is a humanoid full-armored dinosaur whose Gaia Force/Terra Force attack is a Sphere of Destruction.
Adult Garurumon is a blue-fire-breathing wolf, Perfect WereGarurumon is a humanoid martial artist wolf, and MetalGarurumon is a mechanical wolf with ice missiles and metal claws...though it also breathes subzero wind.
Child Patamon fires blasts of air, but all of its evolutions are angels with energy attacks or weapons.
Child Guilmon and Adult Growmon/Growlmon breathe fire, while Perfect MegaloGrowmon/WarGrowlmon is a cyborg with laser attacks and Ultimate Dukemon/Gallantmon is an armored knight.
Dragon Ball Z, but villains most times. Notably Nappa, Piccolo and Cell (whose use of this trope inspired the Internet memes "IMMA FIRIN' MAH LAZER", "SHOOP DA WHOOP", and Dr. Octagonapus, even though he was just screaming in the scene in question).
Frieza, the series' first Big Bad, also used a variant of a breath weapon to gain access to Saichourou/Guru's hut before Nail distracted him & lured him away to fight.
Canon Broly has this ability as well, due to his incredible power being the result of the Oozaru state in his human form.
Taken to the logical extreme with Recoome from the Ginyu Force and his Eraser Gun, who gets shut down (literally) by Krillin upon attempting this on a wounded Vegeta and blows up nearly all his teeth in the process. It doesn't slow him down but it did give Gohan a chance to save Vegeta.
In a technological variant, Sergeant Metallic (aka Major Metallitron) has a missile launcher in his mouth.
And in a particularly hilarious example, Super Buu uses a mouth beam to badly scorch Gotenks, and laughs at him. He's shut up rather quickly when Gotenks opens up wide and delivers the same attack back at him.
Ironically, the most horrifically dangerous breath weapon in the series is used by Dai-Kaioshin (the highest of all the Kaioshins), described as one of the cheeriest and most benevolent beings to ever live. If hit by it, the recipient is immediately diced and then blown up. In the dub, Kaioshin notes that that attack would be a One-Hit Kill on anyone other than Buu, who can regenerate indefinitely. Beware the Nice Ones indeed...
Fullmetal Alchemist (2003): In the final episodes, a cyborg produces a number of guns from surprising places, including a tiny ball turret in his mouth.
Guyver: Some Zoanoids have this; Derzerb of the Hyper-Zoanoid Five could breathe napalm, and the Zoalord De Galenos fires energy blasts from his mouth.
Heroic Age: Bellcross does this several times, being sure to clean up the local space of annoying bug-aliens by using their own life force and energy to power it.
Kaiju Girl Caramelise: When Kuroe first transforms into Harugon, she nearly fires a breath blast at the JSDF helicopters shooting at her, but she stops when she sees Arata looking at her. She later fires off several breath blasts in her human form as an involuntary jealousy-induced reaction to hearing about him interacting with Seina.
Mazinger Z has this as one of its best attacks, the Rust Hurricane. Mazinger blows a jet of particle-charged wind from its mouth grill that corrodes the enemy into nothingness. Its successor Great Mazinger has the Great Typhoon, which is the same thing but without the rust effect, while Super PrototypeMazinkaiser has the Rust Tornado, a version of Mazinger's attack.
Many Robeasts from Mazinger Z, Great Mazinger and UFO Robo Grendizer have breath-based attacks, usually expelling out fire, acid or even poison. One of the seven armies of Mykene Empire (the Reptilian Warbeasts) specialized in this kind of weapons.
The F91 and Crossbone Gundams have a heat vent in place of a "mouth", usually covered by the faceplate. It isn't really intended as a weapon, but if their "overheat" mode activates at point-blank range, the sudden blast of intense heat from the mouth has been shown to damage mobile suits.
My Hero Academia: According to Inko, Izuku's father Hisashi has a fire-breathing quirk. However, the man is never seen on-screen.
The Bijuus are all capable of firing highly destructive balls of pure chakra from their mouths. Several of them also have other breath attacks, such as Shukaku's balls of concentrated air and the Nibi's fireballs.
Unlike the typical example of this trope, Breath Weapons are more commonly used by the heroes; Shizune can breath out poison mist, the Fifth Mizukage can spit acid mist and lava, the Sarutobi clan can all breath fire, Jiraiya and the toads can spit oil, etc. Which isn't to say that the antagonists don't get in on the action; for example, Danzo can fire wind bullets, while the Uchiha antagonists are all fire-breathers as well.
Parodied when Naruto tries to do this while (consciously) using his Bijuu's power. The Hachibi describes it as sort of like vomiting, prompting Naruto to actually try and make himself vomit, which works about as well as you'd think (he wasn't in the right form anyway).
In the first movie, the main antagonist ate the Goe Goe no Minote Literally translated as Voice-Voice Fruit, but referred to in the official subs as Scream-Scream Fruit, which gave him this ability.
The earliest (canon) example is Mr. 5. Using the Bomb-Bomb Fruit, he's able to make any part of his body explode, including his breath, which he loads into a revolver.
Fuza, Shura's giant bird in the Skypiea arc, had a Flame Dial in its beak that allowed it to breathe fire.
Self-made Cyborg Franky's mouth has both a flamethrower and a nailgun.
Bartholomew Kuma had a mouth beam built into him to add on to his other cyborg enhancements. The Pacifista modeled after him likewise have a mouth beam built in them.
In the background, Buggy and Kid both had firebreathers in their crews.
Kaido in his dragon mode has this ability. It is more powerful than anyone mentioned above, as his Breath Weapondisintegrated Oden Castle to nothing.
Kaido's child Yamato has a similar ability to their father, only with what seems to be frost.
Pokémon: The Series: This is one of the most common ways for moves that don't revolve around physically battering an opponent are depicted like: when a Pokémon uses a move such as Hyper Beam, Flamethrower, Dragon Breath or Roar Of Time, it's almost always depicted as a beam of energy or fire coming out of its mouth.
Potemayo: The things on the sides of Guchuko's head shoot a charring variety of beam.
Puella Magi Madoka Magica: Walpurgisnacht is able to breathe fire. At one point, she even sets a building ablaze after tossing it at Homura.
Dragon Race, being a Draconic Humanoid beings, can breathe fire as an attack, as shown several times by Let and Julia.
While transformed by Monster Prison, King can fire out a laser beam from his mouth and perform a sweeping attack with it.
Orochi of Doryu's Specter Team can unleash the deadly Death Poison through the six snakes he wears on his person.
Megido of Magma, one of the Four Demon Kings, can unleash a heat-based beam powerful enough to temporarly block the Endless, the Eldritch Abomination meant to end the world, for quite some time.
Lievre of the Blue Guardians' Six Guards possess the Dark Bring "Hard Breath", which turns his breath into a powerful weapon with gusts strong enough to blow people away and shred clothes.
The Ride-On King: The mouth ray from Dragriffon tunnels through the entire Holy Kingdom's capital.
Rurouni Kenshin : Hyottoko of the Oniwabanshu can use his "Fire Breath" technique to burn opponents. It's revealed that he hides a sack full of oil in his stomach with a nozzle poking in his mouth and flint-covered teeth to create the spark. His fire breathing also loses to Kenshin, who simply spins his sword and deflects the flames with the wind.
Sailor Moon: Flau, a youma from one of the first episodes, was shown to fire lasers from her mouth.
Sgt. Frog has Tamama's signature move, the "Tamama Impact".
Slayers: Most dragons just use old-fashioned fire breath, but gold dragons have laser breath.
Soul Eater: Free's Magic Eye Cannon (despite the name) has him firing a huge laser from his mouth. The reason it's called "Magic Eye" is because he forms the magical energy into the shape of an eye before firing it.
Yu-Gi-Oh!: Several monsters do this, especially Dragon-Types.
There's also the well-known Burst Stream of Destruction / White Lightning from Blue-Eyes White Dragon, and the Giga Mega Flare / Inferno Fire Blast of Red-Eyes Black Dragon.
Sky Dragon Osiris / Slifer the Sky Dragon has two Breath Weapons, one for each mouth. His first mouth fires the yellow Thunder Force (the Japanese name is Chō den dō wa - Thunder Force/Super Electrical Conduction Wave - Thunder Force), aiming for attacking. His second mouth fires the blue Lightning Blast (the Japanese name is Shōraidan/Summon Thunder Bullet), aiming for reducing the ATK or DEF of the opponent's new summoned monster by 2000 points, and destroying them if it's reduced to 0.
Zatch Bell!: Common among the demons, even the ones that look human.
Main protagonist Zatch/Gash is the most prominent example; he channels most of his lightning-based spells with his mouth. Other examples include ice-users Reycom and Furigaro and wind-user Fein.
Bago is a notable example; most demons/mamodos have other spells that they channel without their mouths, but all of his spells are Breath Weapons.
Zoids: If mecha count, you can include pretty much any Zoid with a Charged Particle Beam. 9 times out of 10, the cannon fires from the mouth (with the exception of the Death Stinger).
, Flamethrower