The Authority arc "Godhead" brings us Sister Voice, who leveled Salt Lake City with a powerful rendition of Paul Anka's Puppy Love.
In Buzz!, this is the power of the Spelluminati champion. The sound of their screams is enough to temporarily deafen the Black Queen. It doesn't affect Webster though, because the champion is also his sister and thus he's used to her screaming at him.
In a Darkwing Duck miniseries, one-time character Screaming Mimi could send several men flying backwards with one scream. Alas, she wasn't so useful once they learned to squirt water into her mouth.
Black Canary, member of the Justice League of America and Birds of Prey, pictured on the opening page, with her "Canary Cry", a potent sonic attack able to damage and stun foes or objects, to the point of shattering metal.
Former Teen Titans member Herald gained this power through a super voice box. Unfortunately, as Vox, he can't turn it off — while he can control sound, anything he actually says will kick the ass of everyone in the area.
Accomplished Perfect Physician of the Great Ten has a variation on this; the original Perfect Physician devised a way to use sound to find and heal ailments, using a mere click of his tongue to cure cancers. His successors extrapolated this ability: the second learned to stop earthquakes with a growl, and the third turned back a Mongol horde with a shout. Because the collective memories of the Perfect Physicians are passed on to each new title-holder, successive Perfect Physicians have been able to perform all these feats and more.
The Global Guardians had the Taiwanese Liang Xih-k'ai aka Thunderlord, a Religious Bruiser who could not only use sonic screams but also imitate voices and sounds. His shout could shatter an entire building.
Legion of Super-Heroes: Legionnaire Tyroc has a variety of effects that he can make with a variety of screams (there's a different sound effect for each... effect.)
In Final Crisis, Superman finally kills Darkseid by screaming so loud that the evil god shatters. The effort nearly ruins Supes' vocal cords.
In For the Man Who Has Everything, when an enraged Superman roars Mongul's name upon being freed from the Black Mercy, he shouts so loud that he nearly knocks Robin over.
In The Great Phantom Peril, Faora kicks Superman's neck from behind, forcing him to cry out in pain. His shout's soundwaves accidentally shatter an unfortunate skyscraper's windows.
Long time Superman foe Silver Banshee is not only loud, but if she knows your real name, then hearing her scream results in instant death. She can't kill Supes because she doesn't know his real name, Kal-El. She can still blow out his eardrums, though.
In Last Daughter of Krypton, Supergirl displays this power a couple of times: while experiencing Sensory Overload for the first time, Kara lets out a cry of pain whose sound blast throws her armored attackers away. Later, after confirming that her parents are dead, Kara lets out an anguished, grieving scream whose explosive soundwave overturns furniture, blows machines away and cracks walls.
Post-Flashpoint Supergirl used sonic screams when fighting Black Banshee. He specifically notes it and mocks it as a pale reflection of his own powers, before giving her a demonstration.
In the beginning of Red Daughter of Krypton, Siobhan Smythe has to reluctantly turn into Silver Banshee again to try to hold a berserker Kara back. Her ultrasonic wails can hurt her because they are magic-based.
In Supergirl (Rebirth), Kara is trapped inside a contraption which adapts to her skills. She cannot break free until she realizes she can hear the machine, which means its adaptive cells speak to each other on a specific frequency. Supergirl isolates the sound and then she shouts, flooding the air with the same frequency the adaptive cells use to coordinate countermeasures, deafeaning them so they cannot work together to adapt to her.
In an Action Comics issue, Jon "Superboy" Kent shattered every window in the house by accident while jumping for joy over his father seemingly beating Doomsday.
Banshee Jeanette, of the Secret Six, can leave you comatose with her screams.
The Joker gets this power in a Judge Dredd crossover when he makes a deal with Judge Death to become the fifth Dark Judge. Joker's laugh is now able to blow up people's heads en masse.
Wonder Woman (1987): The Pillar of Pallor cries out and moans so loudly in pain and sorrow that it incapacitates first Diana and later Hippolyta. It is only quieted by the vulture guide Ares sent Hippolyta showing it empathy.
The Swedish comic James Hund once featured the Tibetan Scream Ninjas, who practiced the "especially Oriental" art of screaming buildings apart.
The all-time champion is probably Black Bolt, who can level buildings just by whispering, because his voice isn't just super-sonic, but actually causes massive disruptions in electrons. When he declares war, he's not mixing metaphors. In an Alternate Universe, he committed genocide by yelling at the top of his lungs. However, since he cannot actually control it — as in any whisper from him will destroy buildings, etc. — this makes his position as King of Attilan and leader of the Inhumans extremely reliant on his cousin and wife Medusa's ability to read his body language. He's gotten so good at laser-guided body language that characters have commented on how uncanny it is that they always know what he means. In Marvel Zombies, he managed to wipe out half an army being led by the Incredible Hulk. By saying "Brains", of course.
What If? #34 (the Rule of Funny issue) asked: "What if Black Bolt got the hiccups?" [cue destroyed Manhattan]
X-Men: Sean Cassidy aka Banshee and his daughter Theresa aka Siryn. Screaming also lets them fly, somehow. Oh, and they can talk while using it. Hilarity ensued in the animated series when Banshee had to give Wolverine a ride.
Wolverine: With you making all that noise, we might as well try sneaking into this place with a marching band. Banshee: If you think that's bad, you should hear me sing.
Iron Fist ranks the "Silent Scream" among his "upper-tier abilities". A hypersonic attack that can KO an entire room of thugs, it also leaves him unable to speak for a month.
The Wolverine story "Roar" features a beast whose roar is so powerful it leaves an entire town with bleeding ears, and when Wolverine shows up he has to keep regrowing his eardrums to fight it.
Spider-Man has a couple of characters with this set up.
Most obviously, there's 90s villain Shriek. Her actual offensive use of sound is a sonic beam she fires from her hands, while her scream acts like a Hate Plague.
Phil Urich, the heroic Green Goblin was indicated to have a "Lunatic Laugh" that leaves people stunned in pain and is powerful enough to harm symbiotes, which are weak to sonics. Interestingly, the power was premised on the idea that the Green Goblin (whoever he/she was) had a Creepy High-Pitched Voice, but more recently, the Green Goblin is presented as Evil Sounds Deep. When he return as Hobgoblin he's also back as a cackling, shrieking villain.
B-lister villain the Shocker, despite sounding like he uses electrical attacks, actually uses a harness to create vibrated waves of air that literally shake things apart, leaving him somewhere between here and Blow You Away.
The Queen had this as one of her powers. The force was loud enough to cause Spidey to bleed from his ears, and being in close range of it just twice was enough to knock him out.
Melissa Joan "Mel" Gold debuted as the minor villain "Screaming Mimi", using sonic blasts to commit crimes. When she was recruited for the first iteration of the Thunderbolts, she was outfitted with a cybernetic vocalizer which expanded her repertoire to the point she could create "solid sound constructs", which allowed her to take the new identity of Songbird. She ultimately went straight and became a genuine superhero by that moniker.
In the MonsterVerse spin-off graphic novels Godzilla: Aftershock and Kingdom Kong, the Titans Jinshin-Mushi/MUTO Prime and Camazotz respectively emit weaponized shrieks that can cripple Godzilla and King Kong respectively.
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