The Beatles included bits of studio chatter and noodling around as interstitial material, or even as sound effects within songs on albums such as Let it Be and Abbey Road. Since then, many other artists have done the same. For example, Ben Folds does a few bars of an alternate rendition of his and Nick Hornby's song "Belinda" as a hidden track on the Lonely Avenue album.
Other artists, such as Andy Partridge and Grace Jones, have released their rough demo versions of songs, mistakes and all. The Bang Masters album was basically unreleased material from an an early recording session that was released (against Van Morrison's wishes) by the producer to capitalize on Morrison's later success --the majority of it is not release-ready and includes mistakes and alternate versions of material that would be substantially reworked before release (including, an allegedly revealing version of "Madam George"). The Bootleg Series was a similar release of Bob Dylan's material, although sanctioned by the original artist. Lots of Beatles' alternate takes and original demos are also available.
Some hip-hop recordings deliberately leave in spoken instructions to the producer ("turn up my headphones!") as a stylistic element. Conversely, hip-hop producer Wyclef Jean's spoken instructions to the artists are a signature of his productions. This is similar to James Brown, who actually made his instructions to the band part of many of his best known songs, such as "Sex Machine". There are also some well-known songs that include the spoken count-in (the Beatles again, "Taxman"), or even a false start to the song. The released version of the antifolk song "Wee Ma Moo" by Dufus actually includes the artist saying "we forgot to write an ending," as the musicians trail off awkwardly. Janet Jackson's hit "Runaway" includes the artist light-heartedly chastising herself for an off note near the end ("didn't quite hit that note"). Back to the Beatles one more time: Ringo Starr's imperfect vocals are famously immortalized in the opening lyrics of "With a Little Help From My Friends."