The term "mondegreen" was coined by writer Sylvia Wright in 1954, in an essay she wrote for Harper's Magazine. She wrote:
"When I was a child, my mother used to read aloud to me from Percy's Reliques. One of my favorite poems began, as I remember:
It should be noted that a mondegreen is not quite as simple as a mistake or mishearing: they arise from the verified phenomenon that the breaks a listener hears between words often do not actually exist, but are inserted by the listener's mind (this is why you perceive speakers of foreign languages to be speaking fast and running their words together): had Hendrix actually been singing "kiss this guy," rather than "kiss the sky," it might well have sounded exactly the same, and thus is a common mondegreen with such lyrics.
Intentional mondegreens are a staple of filk, parody, comedy and "novelty" songs; for example, the band They Might Be Giants uses several in their songs as a reference to their childhoods in the 1950s and 1960s. "Weird Al" Yankovic is also known for referencing common mis-hearings of popular songs in his lyrics, often in ways which sound almost identical to the original. This is distinct from the more general use of parody lyrics, as the mondegreens are usually common, pre-existing ones which the lyricist is referencing, rather than a complete invention, as a way of playing with the trope.
The German author Axel Hacke has published various entertaining books about mondegreens. (It also mentions some famous English Mondegreens, like "round John Virgin", "Olive the other Reindeer", "Gladly the cross-eyed bear" and of course the Trope Namer.) Dave Barry also included an entire chapter about misheard lyrics in Dave Barry's Book of Bad Songs.
There's also the related but distinct Soramimi phenomenon, which is when lyrics in one language sound like actual words and lyrics in another language. Finding soramimi (Japanese, vaguely translating to "tricks of the ears") in songs from other languages is such a popular pastime in Japan that one well-known comedy show devotes a regular segment ("Soramimi Hour") to it. For instance, the refrain of the Scorpions' "You Give Me All I Need" was interpreted as "Yukimi onanii" -- "watching the snow fall while pleasuring yourself." A soramimi of "Moskau" by Dschinghis Khan, can be found here.
Several animutations are based around a long series of intentional mondegreens and soramimis, usually involving faux "lyrics" accompanying a confusing (often foreign-language) song. Someone who has read the faked lyrics often has trouble associating the real ones with the song afterwards.
Computer programs that try to understand speech often come up with something like this, from lyrics or just speech, as it's much more difficult for them to distinguish words from each other than to humans. The beta version of the speech-to-text transcriber on YouTube currently works as an automatic Mondegreen generator, often hilariously, when applied to any song there that allows captions.
In July 2008, the 2008 update of Merriam-Webster's Collegiate Dictionary finally enshrined the word "mondegreen" in its pages. To celebrate this momentous event, Merriam Webster Online began soliciting examples from the public as part of a short-lived publicity campaign.
A series of books (and page-a-day calendars) of mondegreens were put together by Gavin Edwards, the first of which is called 'Scuse Me While I Kiss This Guy and Other Misheard Lyrics.
AmIRight.com has a dominating portion of its site dedicated to showcasing an ever-expanding list of mondegreens, likely including those listed here. Yes, you can even submit your own.