> ...I'm thinking more specifically of songs that are based on harmonic
> or melodic material but are ultimately something new.
> What else is out there?

Two that spring to mind:
The Farm - All Together Now (Pachelbel's Canon)
Spiritualized - Ladies and Gentlemen... (Pachelbel's Canon)

There was a sappy 70's pop song with female vocals set to music of Bach (I
think), but the name and artist is not coming to me at the moment.