The Used have quite a few, and actually write damn good slow songs when they're not doing what they're best known for and screaming their heads off. To name a few: Smother Me, Kissing You Goodbye, Tunnel, Yesterday Feelings and Blue And Yellow.
The Red Hot Chili Peppers have quite a few of these, for example: "If", "Porcelain", "This Velvet Glove" (to an extent), "Dosed", "Breaking the Girl", and "Under the Bridge". The latter is a special case as it is one of their most famous songs.
Early in their career they were this trope, with things like "Grand Pappy Du Plenty" and "Lovin' And Touchin'". Now however, they pretty much do this style of song all the time.
AFI's "The Leaving Song" on Sing The Sorrow, and "The Interview" on DECEMBERUNDERGROUND. Same applies to most of "Morningstar" on The Art of Drowning and the verses of "God Called in Sick Today" on Black Sails in the Sunset.
The main difference is that "Fade to Black", "Sanitarium" and "One" are what's usually called "semi-ballads" - they may start as traditional ballads, but around the middle of the song they become a lot heavier. "Nothing Else Matters", on the other hand, is straight-up saccharine ballad.
Megadeth's "Promises" , which is a beautiful power ballad, complete with string arrangements and being based around a Romeo And Juliet theme. If someone else was singing it, you would never know Dave Mustaine had written this song.
Velvet Underground pulled an entire album of this with The Velvet Underground. Part of this was because a lot of the band's gear was stolen, but they also deliberately wanted to make a Lighter and Softer album after the Darker and EdgierWhite Light/White Heat so as to avoid painting themselves into a corner. The trend continued with Loaded, which was their response to their record company asking them to make an album "loaded with hits".
So did Nick Cave with The Good Son, and even gentler with The Boatman's Call and No More Shall We Part.
This was the premise behind Nick Cave's "Lyre of Orpheus," as opposed to its raucous companion piece, "Abattoir Blues."
Similarly, The Jesus and Mary Chain, famous for ear-splitting feedback and concerts that ended in violence, did this with the albums Darklands and Stoned and Dethroned.
"Good Riddance (Time of Your Life)" by Green Day, which is a strong contender for their most well-known song. And before mention it—yes, it is a breakup song, but it's still melodically fitting, and, for a breakup song, it's surprisingly kind. "I hope you had the time of your life..."
"Hello" and "My Immortal" by Evanescence, although the radio edition of the latter (arguably their second most well known song) ends off with a harder sound. (Link to the album version for that reason).
"Swimming Home" is this to their Self-Titled Album and "Good Enough" is this for The Open Door.
Pantera's cover of "Planet Caravan" by Black Sabbath - enough so that the Far Beyond Driven liner notes include a short message from Phil Anselmo explaining to fans (who might not be familiar with the original) that they're just covering a song they like, not attempting to have a pop hit.
The Black Sabbath version itself also qualifies - While Ozzy was singing, their albums almost always included a token ballad like "Changes" and/or a short, pretty acoustic instrumental like "Orchid".
Pantera themselves are not immune to writing gentler songs, "Cemetery Gates" is Pantera's attempt at a Power Ballad and Suicide Note Pt. I is extremely subdued and depressing.
A well-known example is Rise Against having the all-acoustic "Swing Life Away," and "Hero of War".
Not to mention 'Roadside'
"The Last Man On Earth" by Schoolyard Heroes.
"Metaphor" by In Flames is an example of them writing an actual gentle song rather than the folk passages they used on early albums to give the listener's a break. Gentle, understated, melancholic but very bitter and resentful lyrically.
They also have "Come Clarity". "Take me somewhere/don't wanna live/in this dream one more day."
Bad Brains have some, mostly due to their reggae influences coming to the forefront: Their self-titled album, for instance, consists of Hardcore Punk interspersed with a few down-tempo reggae songs ("Jah Calling", "Leaving Babylon", and "I Love I Jah" specifically).
Shadows Fall has "Another Hero Lost", which was written in memory of a dead relative of Brian Fair's that died in Iraq. There's also the acoustic instrumentals that the band always includes once per album.
Flyleaf, while not a loud band at all, has had a few songs that are dramatically more calmer and quiet then their usual songs. Mostly in their first studio album.
The Dillinger Escape Plan have included a few more accessible songs off their more recent albums. They're still very experimental and innovative but make better use of their singer's clean vocal range (something their first singer didn't have.) Tracks like Unretrofied, Black Bubblegum & Milk Lizard sound akin to something a more agressive Faith No More might write.
Early on, gentle Faith No More songs were pretty rare. The early acoustic instrumental "Jim" seemed to have been included for the sake of this trope. Ditto "Edge of the World", a piano ballad written from the point of view of a paedophile. Later on they got pretty eclectic and juxtaposed heavy rock numbers such as "The Gentle Art of Making Enemies" and "Cuckoo for Caca" with gentle numbers such as "Take This Bottle" and "Just a Man". They even had a hit with a cover of Lionel Ritchie and the Commodores' "Easy".
"Come Away Melinda" on Uriah Heep's first album. Especially since the rest of the album is Very 'Eavy (and very 'umble). It's also this song that made them become Uriah Heep (having gone into the studio as a band called 'Spice' and using a session keyboardist on the track made them realise they needed a permanent keyboadist, which led to them changing their name to Uriah Heep)
Glassjaw, normally an extremely loud and aggressive band, has two of these songs on their El Mark Digital EP. "The Number No Good Things Can Come Of", a piano and drums piece, and "Oxycodone", a Lounge-sounding tune with the lead vocalist singing in improvisation.
And now, their latest work, "Daytona White" and "Stations of the New Cross" also count. In fact, most of their Coloring Book album (from which these two songs come from) is this compared to some of their previous work.
"Louder Than Thunder" by The Devil Wears Prada, sung entirely by guitarist/clean vocalist Jeremy Depoyster.
The Melvins are largely associated with grunge and sludge metal, but have a few gentle songs in their repertoire: "Black Bock" is lightly psychedelic folk-rock (albeit with some serious Lyrical Dissonance). The Crybaby includes a pair of straight country covers featuring Hank Williams III (Hank Williams' "Ramblin' Man" and Merle Haggard's "Okie From Miskogee"). And "PG x 3" is an eerie, mostly a capella version of the folk song "Peggy Gordon", inspired by it's use in The Proposition.
Judas Priest: "Angel," "Lost and Found," "Before the Dawn," "Epitaph", "Last Rose of Summer"
"Slumber" from Stranger Than Fiction may also qualify - it resembles an alternative rock song of the loud-soft-loud variety more than it does a Power Ballad, but the verses are surprisingly soft.
Angel Beats! anime band, Girls Dead Monster, usually plays loud and hard (as part of their band's 'distraction creating' intent, but many of their songs do have a quieter version on CD.
The original band leader pulls this off the best with her final song before she disappears with a ballad played on a special acoustic guitar, instead of her normal. My Song
Danzig's Sistinas. While it's technically credited to Glenn Danzig & The Power Fury Orchestra, there's also "You And Me", from the soundtrack to Less Than Zero. Both are Roy Orbison-influenced ballads that show off Glenn Danzig's crooning vocal style, rather than the dark metal he's commonly associated with.
A few of the Paper Chase's songs depart from their usual highly confrontational noise-rock/post-hardcore approach in favor of more melodic, introspective songs, though titles such as "Out Come the Knives" and "At the Other End of the Leash" show that the mood isn't necessarily any different.
"Lost in You" by Three Days Grace, which was a major hit for the group, is a little different from their normal sound to say the least. While the recent album was quite a bit softer than previous ones, this one still stands out.
The point of the Colma album by Buckethead was to give his mother something calming to listen to while recovering from illness. Thus, it is a dramatically different sound from his usual stuff.
Eminem has a few. "Mockingbird", "When I'm Gone", etc.
Metalcore band Demon Hunter seems to pile on more and more of these with every album, but they'd be hard pressed to top their first notable one, the EPIC Tear Jerker "My Heartstrings Come Undone".
Gentleness is hardly a surprise coming from Christian Rock band Disciple nowadays thanks to Lighter and Softer, but "After The World" and "No End At All", both tender God-Is-Love Songs, stuck out like a sore thumb on their mostly heavy album Scars Remain.
"Flower Sun Rain" by Japanese Doom Metal band Boris is very relaxing until the very end, when it builds into a scorching guitar solo accompanied by heavy drum fills.
Portrayed in Spinal Tap with "Lick My Love Pump," Nigel's unfortunately named classical piano piece.
MewithoutYou's Catch For Us Foxes, after eleven tracks of blistering and screaming soundscapes, concludes with "Son of a Widow", which is rather quiet and tender.
The Hives are mostly known for high speed garage rock, but their album Veni Vedi Vicious throws in "Find Another Girl", a pretty faithful cover of a 60's R&B ballad by Jerry Butler. It sticks out quite a bit in the middle of the album.
Black Label Society has Spoke in the Wheel, a very mellow and depressive song that contrasts with other songs sung and composed by bearded, foul-mouthed, pinch-harmonic-crazed Zakk Wylde.
The Black Label Society album Hangover Music Vol. VI' is made up mostly of softer songs that utilize acoustic guitar and piano, meaning that the album really is good music to listen to while hungover.
"In This River", from their Mafia album, was a quiet ballad Wylde dedicated in memory of Darrell Abbott (he'd actually written it months before Abbott's death.
Akercocke has a few parts with clean vocals in their otherwise extremely heavy blackened death metal, but the last song off the album Antichrist - Epode - is fully mellow, beautiful (and is about Satan himself.)
"Spit on a Stranger" by indie rockers Pavement is a ballad (albeit a rather bizarre one) from a band who usually did uptempo songs with Word Salad Lyrics.
Godsmack have "Serenity" off their Faceless album.
Jimi Hendrix had "Castles in the Sand", "The Wind Cries Mary","Sweet Angel", and "Little Wing".
Their other top 40 hit, the relatively obscure "Hole Hearted" was another similar ballad.
Nine Inch Nails did this every now and then, considering that the usual sound of the band is industrial metal. Examples include "A Warm Place", "Lights in the Sky" and "Every Day Is Exactly the Same."
The Christian Hard Rock Band RED tends to have at least two per album, beginning with 'Pieces', and 'Already Over (part 2)' in "End of Silence," 'Take it all away' and 'Nothing and Everything' (Which is an alternate version of the opening song 'Fight Inside') on Innocence and Instinct. While they aren't as intensely loud or grating as bands such as Devil Wears Prada, RED is loud enough to warrant these songs being Surprsingly Gentle.
Motörhead, a band commonly known for being one of the rowdiest, loudest, crudest bands, released a song titled "1916", a slow, mournful song about a young man being killed in battle in World War 1.
A number of Black Metal bands do these, particularly as ambient interludes, intros, or outros. Burzum is a particularly influential example.
Progressive Death Metal band Opeth has several examples, including "To Bid You Farewell", "Credence", "Epilogue", "Benighted", "Face of Melinda", "Harvest", "For Absent Friends", several others, plus the entirety of Damnation and Heritage, both of which qualify as Surprisingly Gentle Albums.
Big & Rich. Their music is country turned Up to Eleven and beyond, and even most of their ballads are loud and flashy. But each of their albums had a softer song: "Drinkin' 'Bout You" on the first (a barroom shuffle), "I Pray for You" and "Never Mind Me" on the second (two mellow, AC-friendly ballads), and "Lost in This Moment" (low-key, mainstream wedding song) on the third. The latter was even released as a single, quickly becoming a Black Sheep Hit and their only top-40 hit on the hot 100.
Emilie Autumn: The Art Of Suicide and Shalott are this on Opheliac.
If I Burn, What Will I Remember, I Don't Understand, Gaslight, Start Another Story off Fight Like A Girl.
Britney Spears: In the break from dancing your ass off, purging your soul sense, she enjoys the ballad section of her tours so they do feature on her albums:
"Where Are You Now" on Oops, "Everytime" / "Shadow" during In The Zone, "Why Should I Be Sad" at the end of Blackout, "Unusual You" / "Out From Under / "Blur" / "My Baby" on Circus and "Trip To Your Heart" on Femme Fatale
The Pretty Reckless have this in the form of You on their debut album, about an unrequited crush.
blur give us "Tender" and "Sweet Song". And from Damon Albarn again, in Gorillaz we have El Manana from Demon Days (though the video is far from gentle) and Cloud of Unknowing in Plastic Beach (and again). On Melancholy Hill is fairly mellow and has very sweet lyrics, so it could fit, but is perhaps too upbeat for this.
Five Finger Death Punch has a few, especially with "Remember Everything". "Walk Away" and "Far From Home" are a couple more.
Though Hüsker Dü gradually got a bit Lighter and Softer musically, "Never Talking To You Again" could be considered one at the time of it's release: an acoustic, folk-influenced (though still bitter-sounding) ballad in the middle of what was mainly a noisy Hardcore Punk album. The album in question, Zen Arcade, also featured a couple of melancholy piano instrumentals, "One Step At A Time" and "Monday Will Never Be The Same".
Avenged Sevenfold has a few of them, particularly "Seize the Day" and "So Far Away". An early example of this is "I Won't See You Tonight Part 2" from Waking The Fallen, when they were still a metalcore band.
Led Zeppelin is a borderline example of this, since probably less than half of their output could actually be classified as "hard rock" — but, after their first two heavily blues-based rock albums, their third album (comprised largely of folk-based music) came as a disappointment to many fans of the band's early work. Especially with "That's the Way".
Guns N' Roses has several, including the four acoustic songs on G N' R Lies, the trilogy of "November Rain", "Don't Cry" and "Estranged" off of the Use Your Illusion albums, and their cover of "Since I Don't Have You" off of "The Spaghetti Incident?".
Usually, The Aquabats! are very excited and energetic...but Hello, Good Night! is surprisingly mellow and thoughtful.
The Monks were a Garage Rock band from the sixties whose music was unusually aggressive for the time, and who were later considered a precursor to Punk Rock. Because their album Black Monk Time wasn't received well at the time, they started going for a Lighter and Softer sound for their last two singles. Their final release "Love Can Tame The Wild" / "He Went Down To The Sea" was especially surprising - the A-side is a sprightly Silly Love Song, while the B-side is a ballad with a seemingly Phil Spector-influenced arrangement featuring vibraphone and trumpet. As bonus tracks on Black Monk Time, these two tracks sort of induce some Mood Whiplash.
King Charles tends to go with orchestral sounds and lots of production. The song Oh England is just Charles, riding in a handsome cab and playing his acoustic guitar while he sings a love song to his home country.
Aly And AJ: "Silence" and "I'm Here" on Insomniatic are both extremely quiet tracks unlike the bulk of the album.
Most EBM and Futurepop acts have at least one ballad per album. Example: Covenant's album Northern Light has "Bullet", a morose Power Balladbut industrialized... Placed in an album with fast-paced songs such as "We Stand Alone" and "Call The Ships To Port".
mind.in.a.box's chiptune album R.E.T.R.O. ends with the power ballad "Whatever Mattered".
The Break Up's aptly titled "Tread Softly".
Tom Petty and the Heartbreakers have "The Best of Everything", a soft piano ballad that fits perfectly into 80s easy listening radio. Petty's solo album Wildflowers is this compared to his work with the Heartbreakers.
Between their second and third albums, Alice in Chains released Sap and Jar Of Flies, two EPs which proved them capable of surprising versatility and restraint. They played mostly acoustic and clean electric guitars and made use of strings as well.
Ministry contributed a surprisingly faithful acoustic cover of "Friend Of The Devil" to the compilation The Bridge School Concerts, Vol. 1 - it turns out Al Jourgenson actually has a smooth, pleasant singing voice when he's not growling and/or running his vocals through distortion and processing.
Dir En Grey's "Jealous -reverse-" is a piano-vocal reworking of their single "Jealous", featuring nothing but Kyo and piano. Also, "Ain't Afraid to Die" is Kyo and piano only until the guitar solos kick in, halfway through the song. Even then, it's still very gentle.
LL Cool J's "I Need Love", which is often cited as being the first Hip Hop ballad.
The techno/electronica musician Cursor Miner has a pop ballad titled "For Each Other".
The Birthday Party's "Jennifer's Veil", from their final EP, is musically quieter and folkier than anything they'd ever done before, and a pointer towards the more tasteful moments of Nick Cave's solo career. (However, it's purely a musical example: the lyrics appear to be about a guy coming back from a war to discover that his girlfriend or sister has been hideously disfigured and probably raped by enemy soldiers.)
Converge has "Phoenix In Flight", off the album Jane Doe, which is very, very soft for being a song by them. But right after that, there comes "Phoenix In Flames", which is just your average Converge song, but harder.
A rare producer-based example. Producer Dann Huff is usually known for his bombastic country-pop arrangements for the likes of Rascal Flatts, with swelling string sections and loads of heavy guitar (Huff is a former member of the rock bands White Heart and Giant, and a session guitarist as well). Even his up-tempos are usually very loud and guitar-driven. But 2013 has seen him moving toward gentler arrangements, as seen in The Band Perry's "Better Dig Two", which sounds surprisingly rootsy; Kelly Clarkson and Vince Gill's "Don't Rush", which sounds like an early 80s country-soul ballad; and Hunter Hayes and Jason Mraz' light, acoustic "Everybody's Got Somebody but Me". Not that he's given up the louder production entirely — The Band Perry's "DONE." is closer to his usual style.