Folk song is as often as not written to existing tunes, or slight modifications of them. This is another very old (and usually non-humorous) kind of musical parody that still continues - for instance Bob Dylan took the tune of the old slave song No more auction block for me as the basis for Blowing in the wind. Some folk tunes have been recycled many times - for instance the melody of Auld Lang Syne.
Classical composers often borrowed folk and popular tunes, as well as making fun of each other's musical styles. Bach and his contemporaries were very fond of the quodlibet - taking popular tunes and playing them in grotesque ways - often combining several of them at once. Haydn (who had a very strong sense of musical humour) was notorious for taking popular melodies and giving them mock serious treatment. Sir Arthur Sullivan was a master of parody of other composers' styles - in the dramatic works he wrote with W. S. Gilbert he parodies at different times the styles of Mendelssohn, Wagner, and even Handel, although (usually) avoiding the stealing of actual musical ideas. As might have been expected, his own music has been parodied ever since.
In the 1940s, Spike Jones and his City Slickers parodied popular music in their own unique way, not by changing lyrics, but adding wild sound effects and comedic stylings to formerly staid old songs such as "Cocktails for Two" and "April Showers." Beginning in 1949, Homer and Jethro did country music arrangements of popular songs, with parody lyrics, such as "Hart Brake Motel" (for "Heartbreak Hotel") and "The Battle of Kookamonga" (after Johnny Horton's "The Battle of New Orleans").
The 1957 Broadway musical Jamaica amusingly parodied the then very fashionable commercial variety of Calypso music. Another musical using a heavy dose of parody was the 1959 show Little Mary Sunshine, which poked fun at old-fashioned operetta.
Other parodists included composer Sir Peter Maxwell Davis, who in 'Eight Songs for a Mad King' (1969) took a canonical piece of music, Handel's Messiah, and subverted it to suit his own needs, in much the same way Hendrix did with 'Star Spangled Banner'; the self-described "piano-wielding fugitive from Harvard", Tom Lehrer; and Victor Borge, originally from Denmark, who switched from a concert piano career to comedy, creating parodies of classical piano pieces and opera.
In 1965, musical satirist Peter Schickele created P. D. Q. Bach, a supposedly newly-discovered member of the J. S. Bach family, whose creative output parodies musicological scholarship, the conventions of Baroque and classical music, as well as introducing elements of slapstick comedy. Schickele continues to tour and record under the pseudonym P. D. Q. Bach to the present day.
And in the science fiction fan community of today, filk music thrives as a source of both parodies and original music, as it has since at least the 1930s, with artists such as Leslie Fish, Tom Smith and Frank Hayes gleefully adapting tunes from many genres to their own varied interests.
Even original artists of the caliber of Tom Lehrer have been known to dip a toe in the waters of musical parody; Lehrer's famous song "The Elements" adapts a tune from Gilbert & Sullivan to the periodic table, and more recently he turned "That's Entertainment" into a précis on his real vocation, "That's Mathematics" (carefully altering the melody to avoid litigation). Other well-known parody artists include The Great Luke Ski, James at War, Sheb Wooley, Tim Cavanagh, Flanders and Swann, Richard Stilgoe, Pinkard & Bowden, Carla Ulbrich, Cledus T. Judd, Chris Moyles (although normally written by Comedy Dave) and Flight of the Conchords.
Richard Cheese and Lounge Against the Machine produces parodies not in the traditional sense of someone like Yankovic, but rather derive their humor from exactly the opposite means. While traditional parody puts new lyrics to largely unchanged music, Cheese keeps the lyrics intact but alters the musical style, thus altering the intent of the song. The humor comes from the juxtaposition of very familiar lyrics from popular Rap, Metal, and Rock songs (particularly containing profane, violent, or sexually explicit lyrics) with Cheese's exceedingly clean, "white bread", campy, lounge style. Me First and the Gimme Gimmes does likewise in a complete opposite manner: they perform hard, sped-up punk renditions of folk songs, soft rock, showtunes, R&B, and other genres not usually associated with punk. Weird Al Yankovic has also ventured into this practice; all but two of his albums feature medleys of either classic rock or then-current hit songs done as fast polkas.
Other notable examples of musical parody in recent years include the 2005 musical Altar Boyz, which parodies both Christian rock and the "boy band" style of pop, the Christian parody band Apologetix, who have targeted popular music from the 1950s to the present, and the Capitol Steps, a group of current and former U.S. Congress staff members based in Washington, DC who focus on politics and other public figures.
Musical parodists were briefly an endangered species again, in the mid-1990s when a case (Campbell v. Acuff-Rose Music, Inc.) was brought before the U.S. Supreme Court by country music legend Roy Acuff's music publishing company against the lead singer of the rap music group 2 Live Crew for recording a lewd version of one of Acuff's songs without his permission. But the justices ruled in favor of the rappers, protecting the fair use doctrine and creating a legal standard for parody as protected derivative work.