Angel: Lorne believes that karaoke is the only way to put things right!
Subverted in the Buffy the Vampire Slayer episode "Hush", in which only a human voice will kill the bad guys, which have taken away everyone's voices to prevent this. Willow offers to play a CD, but Giles informs her it won't do the trick. In "Once More With Feeling," everything happens according to the Power of Rock Showtunes.
The Monkees episode "The Devil and Peter Tork" uses a The Devil and Daniel Webster-style Deal with the Devil plot. Demonic pawn shop owner Mr. Zero claims he gave Peter the talent to play a golden harp in exchange for Peter's soul. However, Zero is defeated when Peter demonstrates that the true source of his ability to play the harp is his love of music.
The Sifl and Olly Show had several of these. One, "Hellfire" ('it rocketh you!') had the titular heroes in a song-vs-song challenge against the Devil. (Subversion: The last words of the song are "Dude, that sucked, RUN!")
A The Kids in the Hall sketch had an aspiring young guitarist face off in a rock duel with Satan, ultimately defeating him with a barrage of Power Chords. While Satan is portrayed as being a much better guitarist than the hero, using six arms to play a blistering solo, the youth nonetheless manages to blow the Devil's mind simply by playing the opening riff of "Smoke on the Water". With a wah-wah pedal.
Sapphire and Steel loved to do this, although they mostly used traditional songs such as sea shanties, army chants, and murder ballads. No monster can resist a rousing rendition of "Drunken Sailor" with the Soul Brotha on lead vocals and the Emo TeenThe Scrappy on backup!
I was working in the lab, late one night, when my eyes beheld an eerie sight, for my monster from his slab began to rise, and suddenly, to my surprise he did the mash! He did the Monster Mash!
In the Doctor Who story "Revelation of the Daleks," the DJ turns his rock albums into an intense sonic beam that he blasts Daleks with.
In the subsequent story Silver Nemesis, the Doctor had built a tricked-out boom box for Ace. At one point the Doctor and Ace use the boom box to broadcast jamming frequencies which disrupt communications among a fleet of Cybermen vessels, while listening to some jazz tapes (the Seventh Doctor is a jazz aficionado).
And in the reboot's take on A Christmas Carol, apparently the Power of Opera works.
Horribly subverted in the failed VH1 show Strange Frequency. The series was basically The Twilight Zone/Outer Limitswith MUSIC! It was a good source of Narm (John Taylor vs. a hotel room! The cast of That '70s Show vs. an evil disco!) for the week or two it was on. But there was one genuinely eerie episode: a rock star attempts to get out of a Deal with the Devil by playing an impossible score that is being written by his own falling blood drops as his ill-gotten guitar's strings snap and slice at his fingers. He barely manages to finish the song when the (very irritated) devil points out that he missed a tiny symbol at the end, which means "repeat from the beginning". Cue evil laughter/Big "NO!".
This trope also provides a kick-ass example of Crowning Moment of Awesome for the Ho Yay-laced band Jeffster in the second-season finale of Chuck, when Chuck and Morgan (who are Heterosexual Life-Partners, and how!) that 'We Need a Distraction' so he can get his sister out of danger - and Morgan has the band (backed up by a string quartet) do a world-class cover of Styx's 'Mr. Roboto' in the wedding chapel! They rock the church so hard, nobody hears a bit of the running gun battle in the reception area between a Special Forces team and the bad guys! The absolute most kick-ass moment - when one of the group sets off fireworks in the chapel. A reviewer of the episode said that the episode had so much concentrated awesome that it may be illegal in several states.
Done again in the series finale. Quinn has set a bomb to blow up in a concert hall once the final note of a song (part of the New World Symphony) ends, and Morgan and Casey need to buy Chuck and Sarah time to get the codes needed to shut it down. Jeff and Lester, who are now aware of their identities, show up and Morgan gets an idea. Just as the final note of the concert fades out and the bomb is set to explode comes the strains of A-Ha's "Take on Me," gaining Chuck and Sarah just enough time to deal with Quinn and stop the bomb. Epic.
Kamen Rider Hibiki has music as the series theme and the Riders use music based attacks to finish off enemies. Falling more squarely in this trope, we have Todoroki, who uses a guitar (as did his mentor Zanki). When he visits Hibiki's world in his own series, Ditto FighterDecade joins the fun by finishing off a literal Giant Enemy Crab in an epicjam session.
The Capricorn Zodiarts from Kamen Rider Fourze applies for this trope, and not just Instrument of Murder, because of his other powers. Not only does he go from pretty good to Epic Rocking, but his music benefits others, as shown when it allows his old friend J.K. to sing well and when it powers up the Switches of his fellow Zodiac-level Zodiarts.
Another Toku example is Zyuden Sentai Kyoryuger, wherein it's explained that music has always had a positive effect on dinosaurs, and humans giving it the gift of rhythm helped guide them in the right direction. Hence why they are Dance Battlers, and a soothing melody has the power of, among other things, awaken Zyudenryu from long hibernations and bring Torin back to life.
The 10th Kingdom easily shows that We will rock you is the best song about sheep ever. Despite having nothing to do with sheep.
Notable episodes of The Aquabats! Super Show! that use this trope include "EagleClaw!" and "Pilgrim Boy!". The former has Eaglebones Falconhawk squaring off in guitar duels with his brother EagleClaw and the latter has the shapeshifting Pilgrim Boy defeat a giant potato bug by singing a touching power ballad.
In the Tenacious D TV series, the "Tribute" sketch has the boys tell a tale of defeating a demon by playing "the best song in the world," which is implied to be "Stairway to Heaven."