The Pet Shop Boys song "The Night I Fell in Love" blurs the lines between this and Take That; a parody of the homophobia both inherent and explicit in the songs and public persona of Eminem by imagining him having a homosexual affair with a starstruck young fan, the song is written in a gentle, sweet fashion that is more teasing than anything else. Eminem's response, however, was a bit less gentle; at one point in one of his songs he runs them over with his car. Someone's a bit touchy, it seems.
Artists take the occasional potshot at Mr. Mathers because they know that, no matter how mild or teasing the shot, he'll double the publicity for them by completely overreacting.
Is it Mathers overreacting because he's genuinely insecure, or is he overreacting because it's all part of the act?
Unlike Bob Rivers, Weird Al's parodies usually seem to have a touch of class in them, even those that make fun of the singer directly, like "Smells Like Nirvana". He does it well enough that even the artists he parodies like his work; Kurt Cobain, for example, loved "Smells Like Nirvana". It helps that Al asks first (which is why he's never parodied a Prince song — Prince Rogers Nelson always says no).
"Weird Al's Traffic Jam is a parody of Prince's music style.
Conversely, Michael Jackson found "Fat" and "Eat It" (parodies of Bad and Beat It respectively) to be so hilarious (even going so far is to lend him the same sets from his videos to make new ones), that he gave Weird Al permission to parody all his songs, as well as all future songs.
With the exception of ("Snack All Night") (Black or White), which Jackson said was too serious a message, though he still performs it live.
He did get in trouble with Coolio for "Amish Paradise", for unclear reasons. Apparently, Al's people talked to Coolio's people, who said yes, but Coolio HIMSELF didn't approve it. (And got angry about it.)
When he found out about Coolio's response, Al apologized, like the class act he is. Eventually, Coolio got over it too, and gave Al a hug.
Something similar happened when Al wanted to do a parody of James Blunt's "You're Beautiful". Apparently Al was granted permission to do the parody, but after he'd recorded "You're Pitiful", Atlantic (Blunt's label) refused the permission, so Al dropped the tune from his latest record. However, he still performs it (and a few other refused parodies) live.
Not only does he perform "You're Pitiful" live, but he also released the song for free, just as a Take That against Atlantic.
Notably, when Weird Al asked Mark Knopfler for permission to parody Dire Strait's "Money for Nothing" as "Money for Nothing/Beverly Hillbillies," Knopfler granted the request with the condition that Knopfler play the guitar part himself.
Likewise with his Doors style parody, "Craigslist," Ray Manzerek requested to play the synth part himself.
The liner notes of the Alapalooza album state that all royalties from "Achy Breaky Song" go to a children's charity. The song is harsh by Al's standards, as it is one of the few songs of his that sends up the original song itself; the charitable donation may have been a stipulation of Billy Ray Cyrus.
Another example of a parodist who usually does his parodies with love is Cledus T. Judd. Like Weird Al, he always asks the artists' permission. The only artist who ever turned him down was Garth Brooks, who initially declined to let him parody the Trisha Yearwood duet "In Another's Eyes" but later changed his mind. Judd has also gotten the original artists to help him out several times.
The above three examples all originated as TV or movie mockumentaries, but the music parodies are good enough to stand on their own.
Massacration is a similar (but even more awesome) example. Originally created by Brazilian comedy group Hermes & Renato to star in a music video making fun of Heavy Metal band conventions (such as Brazilian metal bands singing in English, or the emphasis on macabre imagery in lyrics and clips), they ended up becoming quite successful as a real Heavy Metal band, even though they're still spoofing the genre; they've even released albums and opened shows for serious bands, like Sepultura.
The Hee Bee Gee Bees spoofed numerous artists of the 70s and 80s. Now sadly almost forgotten.
P.D.Q. Bach—supposedly the talentless, ne'er-do-well son of Johann Sebastian Bach (1807-1742?). Many albums of P.D.Q. Bach's music exist (performed by classical musicians). There's also a biography. They are actually the creation of Peter Schickele, who is far better known for P.D.Q. Bach than for the serious classical music he composes.
"Bach Portrait", on a P.D.Q. Bach album but credited to Schickele, is an Affectionate Parody of Aaron Copland's "Lincoln Portrait".
The band Flight of the Conchords has produced several songs which are parodies of certain types of music. "Think About It" for example, parodies music which uses the desolation of the modern world as subject matter.
Specific examples: "I'm Not Crying" - (10CC - "I'm Not in Love"); "You Don't Have to be a Prostitute" (The Police - "Roxanne"); "Inner-City Pressure" (Pet Shop Boys - "West End Girls").
And then, of course, there's "Bowie", which needs no explanation.
"Sylvia's Mother", written by Shel Silverstein and performed by Dr Hook & The Medicine Show, could be considered an affectionate parody of heartbroken teenage love songs.
Da Vincis Notebook has their song Title of the Song, which parodies any/all boyband love ballad. How do they do so? They sing in verse what typically goes into the song at that given point. Including when the singer should "drop to their knees to elicit a crowd response" and "hold a high note".
For those who don't get the joke, Title of the Song refers to whatever the song would be stereotypically called by a given band, the title of which is often used as during the refrain of the song. Basically, instead of writing a boy-band love ballad, they sing the how to of writing a boy-band love ballad.
Paul and Storm (a duo consisting of two former members) have a number of these as well. Most notable are their RandyNewmanTheme Songs, but they also have "John Mellencamp's 'Theme from 24'", and a series of supposition songs ("If James Taylor Were on Fire" "If Bob Dylan Were Hiding at the Bottom of a Well" "If James Taylor Were on Fire at the Bottom of a Well" "If Leon Redbone Suffered a Debilitating Head Injury" "If Aaron Neville Were Waiting for a Parking Spot at the Mall But Someone Else Snagged It" and finally "If They Might Be Giants Were the Ice Cream Man").
Once, for the Masters of Song Fu competition, Paul and Storm were asked to do a song in the style of their friend Jonathan Coulton. The result was the song "Live", which used the "mad scientist in love" theme that was part of some of Coulton's songs, most notably "Skullcrusher Mountain". Coulton returned the favor (as part of the same competition) with the song "Big Dick Farts a Polka".
Freddie Mercury's "The Great Pretender" video spoofs his band Queen's past music videos, and Mercury's image as a Large Ham.
The Blue Man Group song "It's Time to Start" parodies rock concerts by explaining what rock concert tropes the audience should carry out, ranging from the realistic ("Rock Concert Movement #1, the basic head bob", and "#2, the one-armed fist pump") to the ridiculous ("#4, the behind-the-head leg stretch", which the Blue Men proceed to actually do). #3 ("the up-and-down jumping motion") receives a step-by-step explanation, though in live performances it's been replaced with #10 ("getting a closer look at the audience") which involves footage from a miniature camera supposedly being shoved down an audience member's throat.
Kompressor's work affectionately parodies industrial music.
Anna Russell's parodies of popular and classical music varied widely in their sincerity. In her "Survey of Singing from Madrigals to Modern Opera," though the parodies of madrigals and coloratura arias are too silly to be true, "Wir gehen in den Automaten" could be mistaken for a Bach cantata if the lyrics weren't about ordering bacon at the Automat, and "Aria from 'The Psychiatrist'" only sounds insane when compared with Magda's aria from The Consul and its repetition of the question "What is your name?"
Frank Zappa and the Mothers of Invention recorded an album entitled "Cruising with Ruben & the Jets", an affectionate parody of fifties doo-wop music. The result was so authentic-sounding, many people mistook the songs for another band entirely, causing the album border on an Indecisive Parody.
As "the greatest fake MCs on Earth," The Lonely Island have taken everything they love about rap, hip-hop, R&B, and club music for the sole purpose of making songs about making dookie your pants, having sex with piles of manure, premature ejaculation, and most importantly, the Space Olympics.
The Dukes of Stratosphear was XTC's send-up of psychedelic rock, an influence which would later start being more prominent in their non-parodic work: Songs usually were in the style of specific sixties groups - most obviously "Bike Ride To The Moon" parodies Syd Barrett-era Pink Floyd, while "Brainiac's Daughter" and "The Mole From The Ministry" parody The Beatles. Production-wise, they incorporated a lot of Gratuitous Panning.
At one point Andy Partridge wanted to do something of a Spiritual Sequel dedicated to bubblegum pop of the same era - it never ended up happening, but one such song ("Cherry In Your Tree") turned up on a Carmen Sandiego game soundtrack, while two others ("Candymine" and "Visit To The Doctor") were on Partidge's demo compilation Fuzzy Warbles Volume Seven.
The Backstreet Boys put out a music video for their song "I Just Want You To Know", in which they parodied 80's Hair Metal by playing one such band named Sphynkter, as well as playing fans of said band.
In the behind-the-scenes for Lindsey Stirling's Assassin's Creed III medley, one of her crew dances about in a parody of her own moves, whilst holding two sticks to imitate bowing a violin. Everyone ends up laughing, though Stirling also pretends to be indignant and say she doesn't look like that.