The 1st/2nd Edition androsphinx had a roar that could cause Hit Points of damage (in addition to deafening, fear, loss of strength, paralysis and being knocked over) to anyone close by.
Third edition D&D officially includes "sonic" as one of its energy/damage types and provides spells, magic items, and monsters that make use of it. (In 3.0 and 3.5 at least it was arguably one of the more effective damage types because few creatures had inherent resistance to it — unlike, say, fire or cold — and an object's hardness would not protect said object's hit points against it.) This is to say nothing of effects that invoke the trope but don't technically do sonic damage, such as "Wail of the Banshee".
Savage Species introduced at least one Feat that did stuff like this. Sadly, most of these required you to be at least Large, if not Huge. Blowhard could literally bowl over your opponents. It was also restricted in that you couldn't combine your breath weapon with it.
4th edition has "thunder" damage, which is basically sonic damage with a more "fantasy appropriate" name. This change remained in 5th edition.
Of course, the epitome of this trope is the Shout spell, with its sonic damage, deafening, and object-shattering effects...all with just one very loud noise.
Noise Marines mostly use their Blastmasters or Sonic Blasters to tear apart enemies with The Power of Rock, but the Doom Siren weapon — appearing as either an amplifier over the mouth or a backpack-mounted mini-pipe organ — allows vocalists to get kills too.
Slaaneshi daemons have the Warp Scream ability that paralyzes foes with fear.
The Night Lords use deafening shrieks and cries to disorient and incapacitate their targets.
EldarHowling Banshees have amplifiers built into their helms that make their screams into effective sonic weapons.
A Nobilis character with enough points in Aspect can (with effort) shout loud enough to kill someone, and with a little extra push, deafen entire countries.
There are weapons in GURPS: Ultra-Tech, appropriately called "screamers", that can melt a person with soundwaves.
In Cybergeneration, a spinoff of R. Talsorian Games' Cyberpunk, you could play an "Evolved" character which is basically a kid that's been enhanced by nanomachines that are spreading like a virus. The supplement MEDIA FRONT gave us an Evolved type called Jammers whose modification was that their throat, eustachian tubes and ears were replaced with a non-newtonian, metallic super-carbon polymer kind of like living mercury. In addition to the standard screaming, they could alter their throats to mimic any sound, or sounds, use the vibrations in their voice to hypnotize or persuade, and modify their ears to enhance their hearing.
One of the character classes in Orpheus is the Banshee Shade. The base skill, Wail, ranges from causing subtle changes in emotions to ripping apart someone's body and mind with a scream.
This itself is a take on the Keening Arcanos from the predecessor game, Wraith: The Oblivion. Practiced by the Chanteurs, it also ranged from emotional manipulation to rending someone's corpus with a shout.
Gamma World. In 1E the Sonic Attack Ability mutation damaged all creatures within 10 meters.
Stormbringer. The Stormbringer Companion had the Crimson Xoar, a gigantic (60+ feet high) water buffalo whose bellow could damage the blood vessels and tissues of anyone within a mile of it.
Supplement All the Worlds' Monsters Volume III. The None Such is a cross between a blink dog, a Greater Demon and a phase spider. It can give off a scream that causes 1-12 Hit Points and stuns opponents for 1-3 melee turns.
Arduin RPG, The Compleat Arduin Book 2: Resources. The Blue Bellower is a giant metallic blue rhinoceros beetle. It can bellow so loudly that it has a 35% chance of deafening the unprotected ears of anyone nearby.
In Vampire: The Masquerade a Daughter of Cacophony can use the bloodline-specific discipline of Melpominee to create all sorts of effects and damage through their voice. The truly damaging ones are granted at about 4 dots.