I foresee that this will become an extensive thread. š
Judging Amy: of the DVDs that have been released, numerous alterations have been made to the soundtrack.
Heartbeat: the soundtrack which includes songs by the Beatles and countless other artists who had 60s hits has been altered for the DVD releases.
The UK R2 DVD for season two of Frasier completely removes the scene where Great Balls of Fire is played on the piano. It is uncut on the US R1.
Marriedā¦ With Children: Sinatraās āLove and Marriageā was replaced with an instrumental track on the season three but it has been restored on the Mill Creek DVDs. h/t: crissrudd4554
Quantum Leap: the DVDs contain numerous replacements to the soundtrack. Howeverā¦ h/t: SpacemanDoug
The blu-ray releases restore the music in both the US Mill Creek release and the UK Fabulous Films release, however both releases are not 100% the same
On the US Mill Creek release, the episodes Genesis, Lee Harvey Oswald, and Trilogy Parts 2 and 3 (originally parts 2 and 3 were edited together into one movie) are presented in their syndicated two part versions, as the original NBC versions were movie versions. On the UK Fabulous Films release, Genesis and Lee Harvey Oswald are both restored to their original movie versions, however parts 2 and 3 of Trilogy still remain in their split form.
From what I know, the original movie version of Trilogy Parts 2 and 3 have never been seen outside of the original NBC broadcast, and even the original Universal DVD releases had it split into the two part version (though the same DVD release presented Genesis and Lee Harvey Oswald in their movie versions).
American Dreams: according to the executive producer, 20% of the original soundtrack has been replaced for the DVD with songs that were cheaper to licence.
Top Gear: numerous replacements with library music.
The Take: as above.
Life on Mars (UK): substitutions of songs.
New Tricks: the song Mellow Yellow was removed from a scene in the first series.
Catherine Tate: a sketch in series one no longer works due to a soundtrack substitution.
Super Mario Brothers Super Show: substitutions of the original music for the DVD release.