Song Parody

A song parody is a a specific form of parody that involves taking an existing song, keeping the beat and background the same, then rewriting the lyrics (or possibly adding lyrics to a song that originally had none). Sometimes the new lyrics are similar to the original, sometimes they bear little resemblance. The United States Supreme Court case Campbell v. Acuff-Rose Music established song parodies as Fair Use, even when used for profit. Thus, one does not technically need to get permission from the original artist to make a parody, though some (such as "Weird Al" Yankovic) make it a point to get permission for any parodies.

In a non-audio medium such as a comic, making a song parody can be a good way to let the reader know how a song is supposed to actually sound by giving them a beat and tune to which it should be set as he reads the lyrics.

Live Action TV
"On the first day of Christmas My true love gave to me A drunk who drove into a tree On the second day of Christmas My true love gave to me Two shattered skulls And a drunk who drove into a tree....
 * Stargate 's creators made a version of the opening theme with lyrics.
 * That Mitchell and Webb Look mentioned a the existance of a secret Snooker-based parody of "Lady in Red" in one sketch about two Snooker tournament radio commentators. In a follow-up sketch later in the episode, the two commentators actually sing a portion of the song, "Table of Reds", in dedication to a manic-depressive Snooker player whom the commentators had both saved from committing suicide at one time or another. See the full sketch here.
 * The first season Christmas Episode of Scrubs gives us this cheerfully morbid parody of The Twelve Days of Christmas, which plays over a montage of Turk's spirit breaking over the course of a terrible Christmas Eve spent on-call:

Twelve beaten children Eleven drive-by shootings Ten frozen homeless Nine amputations Eight burn victims Seven strangled shoppers Six random knifings Five suicides Four beaten wives Three O.D.'s Two shattered skulls And a drunk who drove into a tree!"

Magazines

 * Mad Magazine sometimes does this, with a Note From Ed mentioning the tune to which the lyrics are set.

Music

 * "Weird Al" Yankovic has based his career on this trope.
 * Many filk songs are parodies of other songs.
 * Liam Lynch's album Fake Songs: There's the "Fake Bjork Song", the "Fake David Bowie Song", etc.
 * Cletus T. Judd, like Weird Al, does mostly song parodies, focusing on country music.
 * Christian band Apologetix performs Christian parodies of popular songs.
 * Comedy-themed barbershop quartets often have entire repertoires that consist of parodies of popular barbershop songs.
 * Allan Sherman is an older example of building a career on parodies.
 * Anthony and Those Other Guys Thormas Time is a Jingle Bells Parody.
 * Self primarily do non-comedic originals, but the outtake compilation Feels Like Breakin' Shit included a pair of parody songs: "Titanic" is a Titanic-themed parody of The Pixies' "Gigantic" (which also includes a bit of Weezer's "The World Has Turned And left Me Here"), while "Moronic" is a parody of Alanis Morissette's "Ironic" that's a Take That to the original artist.
 * "Puppet Dude" by Foetus is an odd case of a stealth song parody: If you read the lyrics, they're clearly meant to fit the meter and rhyme scheme of "Rocket Man", but the song itself sounds absolutely nothing like it.
 * Garfunkel And Oates parodied their own "I Would Never (Have Sex With You)" as "I Would Never (Dissect An Ewe)", while pretending to be an amateur tribute act called Simon And Hall.

Web Original

 * This trope is the entire premise of the Key of Awesome.
 * Little Kuriboh has done several song parodies using the cast of Yu-Gi-Oh!: The Abridged Series.
 * Some College Humor sketches are song parodies, such as "Don't Stop Your Screaming" or "Sing Talk".
 * Pen Of Chaos made some, in Le Donjon De Naheulbeuk, mostly by taking old traditionnal songs like "Belle qui tiens ma vie".

Web Comics

 * Elan parodies "O Danny Boy" In this Order of the Stick comic.

Western Animation

 * Many of the songs on Animaniacs were parodies of already existing songs. The episode "H.M.S. Wakko" was made chiefly of parodies of Gilbert and Sullivan songs.