I foresee that this will become an extensive thread. 😃
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.
Married… With Children: Sinatra’s “Love and Marriage” was replaced with an instrumental version on the season three DVD.
Quantum Leap: the DVDs contain numerous replacements to the soundtrack.
Northern Exposure: as above.
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.