The several members from the village of Sound in Naruto, although none of them make the noise with their own voice.
The Tailed Beasts can flatten forests, cause tsunamis, and send almost everything in front of them flying with their powerful roar. That is, when they are not using their tails, feet, or Tailed BeastBombs.
When Grimmjow Jaegerjacquez performs his release, the first thing he does is howl loud enough to throw up gale-force winds and momentarily stagger the protagonist.
Wonderweiss destroys the ice imprisoning Harribel with his creepy shrieking.
Jerome Guizbatt does this to the point he's codenamed "The Roar". It renders Kenpachi temporarily deaf.
Several martial artists in Kenichi: The Mightiest Disciple are able to do this. Siegfried knocks one of his opponents unconscious by screaming at a hellish pitch, Silcardo Jenazad can cause an avalanche with his voice, and the Elder at one point screams with enough force to knock over everybody in a stadium - while the Elder's strength was limited to 0.0002% of his usual power.
Scrapped Princess: Pacifica doesn't have the capacity to fight like her adopted siblings, but whenever tragedy strikes around her (people dying, people trying to kill her, etc.), she emits a scream that sends out a massive shockwave. It doesn't kill anybody, but it is useful for breaking them free from mind control. It's because her powers as the anti-Peacemaker program only trigger under extreme stress.
In the spirit of the series' ridiculous power levels, Buu in Dragon Ball Z uses this to escape confinement in another dimension (it was partially out of desperation — there wasn't any candy there). Later, Gotenks powers-up and replicates the shout to escape the same dimension.
Buu later attempts to destroy the whole of creation in a similar manner, and is only barely stopped by Vegitto (the only time in that entire fight that had Vegitto looking worried... or showing any kind of effort for that matter).
The Suzuki aliens from Gantz have an attack that is basically this in beam form.
Ragnarok in Soul Eater has this ability, known as Screech Alpha. There is a Screech Beta and a couple others also. Probably about half Ragnarock's named attacks involve screaming.
This trope is Crona and Ragnarok's entire schtick, pretty much. Other meister-weapon teams use a technique called 'Soul Resonance' to power up: Crona and Ragnarok use Scream Resonance.
Black*Star disrupts it with a roar of his own.
And Crona tops it to cover the ENTIRE MOON in screams.
Lala in To Love RU knocked a typhoon off course by yelling at it....because it was gonna ruin her trip to the beach. It's one of the few opponents she actually seemed to be angry at.
Corpse Princess had a Shikabane whose scream could propel a human several metres, and make bullets explode.
The Iron Howl spell in Lyrical Nanoha, which works like a flashbang grenade minus the flash, stunning all unprepared people within the area. This is actually more like a magical version of Sonic Stunner.
In Mahou Sensei Negima!, the first team that Negi and Kotarou faced as prize fighters in the Magic World included a Tiger Man capable of emitting a roar powerful enough to match Negi's Beam Spam.
The title character in Betterman uses this when he transforms into his Nebula form. The frequency is tuned to the specific enemy he's fighting, so bystanders are left unharmed.
In the finale of the '80s Astro Boy, the final robot, "Bora", has this ability.
Kamen no Maid Guy gives us MAID GUY VOICE. It's capable of preventing people from moving.
Kanade Kamiya of Rosario + Vampire is a Siren, using his songs to cause unbearable pain to all who hear it, as well as allegedly having songs for brainwashing. San Otonashi is a Siren who decided to not talk because of what her powers did when she was younger, using a sketchbook to communicate. She uses her own songs to protect the heroes from Kamiya, but at this point she still remains fairly uncommunicative. When she starts talking, you are already dead.
Ryu Kumon, a foe of Ranma whose fighting style has a paralyzing scream due to surprise. It's usually something like "FREEZE!", but can be anything suited for his enemy. "LOOK! YOUR MOTHER!" (It Makes Sense in Context)
Natsu inFairy Taildefeats an enemy who can hear people's thoughts, by roaring very loudly.
In Acnologia's first appearance, he roars loudly enough that the ground in front of it gets torn up and trees get uprooted. Note that this is just Acnologia bellowing, not an actual attack.
In Toriko, the fourth and final member of the Four Heavenly Kings to be introduced is a colossal man called Zebra, who takes this power Up to Eleven, demonstrating the ability to use echoes to generate an artillery barrage and even more or less nuke countless powerful monsters with a single shout.
He can also manipulate soundwaves in ways that make no sense, such as protecting himself with a wall of sound, and giving someone else persistent armor made of sound by shouting from hundreds of yards away.
Yuuki of Code:Breaker has the power of sound: he can hear exceptionally well and control sound, which means he can pack quite a punch with his sonic booms and even move at the speed of sound. He's considered one of the most powerful Code: Breakers.