Barbari÷n - My Rock. You've got the Grim Reaper on drums, barbarians playing guitar, a kid with a patch jacket, thunder and lightning, soaring vocals, large beards, the ability to yell so epically that it knocks a dissenting father through the wall, turns the mom into a groupie with a ripped up shirt and miniskirt, and lifts the house from its foundation into Valhalla. Fucking Metal.
U2: Elevation video shows Bono and The Edge fighting the Big Bad from the first Tomb Raider movie with a shockwave created by Edge's guitar.
DragonForce: Operation Ground and Pound shows the band fighting off a fleet of enemy spaceships with the power of metal. (Yes, that guy did just shoot a bolt of lightning from his keytar.) There's also a guitar duel. Subverted, because most of the actual fighting takes place inside a video game played by guitarists Herman Li and Sam Totman.
Also, in the video for Heroes of Our Time, the band appears to power a fleet of rockets with their music.
And then in The Last Journey Home, they blow up part of Los Angeles by rocking out too hard.
The music video for Dokken's "Dream Warriors".
The Jon Spencer Blues Explosion: "Burn It Off" has the band members using The Power of Blues-Influence Rock 'n' Roll to defeat various Ray Harryhausen monsters.
Using the power of rock to lead humanity into Nirvana would have been the plot of Pete Townshend's Lifehouse film, had it been produced when he first conceived of it in 1970. The project was ultimately released as a radio play in 1999, but its story was vastly different.
During live performances of "Octavarium" and "The Dark Eternal Night", Dream Theater shows short films of their animated selves fighting monsters with their musical prowess (or in the case of drummer Mike Portnoy, the power of his saliva).
The StyxRock Opera/Concept Album "Kilroy Was Here" featured a dystopian future where the Culture Police have outlawed rock and roll. Dissident Robert Orwin Charles Kilroy, newly freed from prison, sets out to spark a revolution the help of an electric guitar, a synthesizer, and an arsenal of 80s power chords.
Subverted in the music video for "Fashion Zombies!" by The Aquabats!. The superhero band is chased around by teenager gangs dressed in various fashion trends: 80's, goth, punk, prep school, etc. When cornered they whip out their instruments and proceed to rock. Once they've finished with the song, the teenagers descend upon them. When the crowd recedes, the Aquabats have been transformed into fashion zombies.
Let's not forget the Charlie Daniels Band song "The Devil Went Down to Georgia"!
Rush's 2112. However, the protagonist doesn't succeed by himself and ends up killing himself before seeing the Solar Federation overthrown.
In Hammerfall's video for the song "Hearts on Fire", they defeat an army of skeletons by using their music to summon a circle of runestones and cast a rather apocalyptic-looking spell.
The Music video for Earthquake by Labrinth has multiple shots of him waving his arms about causing shock-waves of bass, while the lyrics liken this to "dropping bombs leaving rubble and dust".
Finnish band Lordi in the video for their song "Hard Rock Hallelujah" use the Power of Rock to knock down part of a school gymnasium, transform a cute Goth girl into a sorceress, and, most importantly, kill people and resurrect them as zombies.
"Rock the Casbah" by the Clash is about a rock band inspiring a military coup in a middle-eastern country very similar to Iran.
In the music video for Dokken's "Dream Warriors", the band fights off Freddy Krueger. And it gets better, the whole video turns out to be a nightmare that Freddy is having.
And in the "Breaking the Chains" video, George Lynch can LITERALLY break chains via his guitar solo.
We would be remiss not to mention one instance of the Power of Rock being an evil power, in its capacity to bring the dead back to life...for one of the most awesome music videos ever. Michael can't get enough of this power he seems to have over the dance floor.
British comedy jazz-funk-lounge-rock merchants Pillow Talk have a song called "Doctor Roland Parker Versus the Defibrillator", in which Dr Roland Parker (their bassist) defeats a monstrous killer defibrillator with "the awesome power of the bass".
Roger Waters' song "The Tide is Turning" was a tribute to Live Aid, and perhaps a tribute to this trope. "I'm not saying that the battle's been won / but Saturday Night all those kids in the sun / rescued technologies sword from the hands of the warlord". Does equal time as a Protest Song as well
Dream Theater occasionally have cute animations playing in the background when they play some songs live of them turning zombies into happy people/defeating wolfmen/scaring spiders away/saving James LaBrie (more's the pity) through their elemental powers of music.
The Protomen's music has been noted to rout armies of killer robots and save doomed cities. If they can't quite handle the job, their fans have been known to help.
Don't forget their drummer The Reanimator, who destroys his sticks in every show (then throws them into the audience) and destroys drumheads quite regularly too.
Subverted by Boombox; the titular boombox makes people chill out, cease being enemies, dance, etc, which works fine at a dinner of the rich and privileged, and fine in the streets of New York, but at an old-folks home, the effects are rather unfortunate.
A boombox can change the world. / You gotta know your limits with a boombox. / This was a cautionary tale. / A boombox is not a toy.
In the music video for Damn Yankees' "Higher Enough," Ted Nugent repels bullets with the power of his guitar solo. Patton Oswalt based a comedy bit around noting the use of this trope in the video, hoping that dumbasses would actually try it.
Twisted Sister. Specifically, their videos for "I Wanna Rock" and "We're Not Gonna Take It," in which being a heavy metal fan gains you absurdly godlike powers.
The Damned Things in We've Got A Situation Here. The band discovers how use the Power of Rock to shoot laser beams. They use that to "rock" Wallstreet, unemployment problems and even the junk size of men, and turn evil assailants into HOT punk rocker chicks.
Status Quo released a song called The Power Of Rock - years after the idea had already become a cliche, but somewhat redeemed by having most of the song in a surprisingly slow tempo. They later took this a step further, releasing Rock Till You Drop (their own song, not a cover) which was a slow, folky 3/4-time ballad.
During live shows, usually during the self-titled song, Iron Maiden's mascot Eddie shows up in robotic form and fought off by the band (Nicko Mc Brain, the drummer, throws drumsticks, whereas the guitarists beat him with guitars and play in his face).
In the video to Les Rhythmes Digitales' "(Hey You) What's That Sound", Jacques Lu Cont zaps passersby with a keytar, turning them into their more-inclined-to-dance The '80s equivalents - for instance a group of teenagers loitering by a convenience store become boombox-wielding breakdancers. This all leads up to a massive eighties dance party in the streets.
Twisted Sister has this in several of their music videos, including "I Wanna Rock" and "We're Not Gonna Take It", where a cruel school teacher or father is literally thrown through windows and walls by the Power of Rock.