Modern Covers of Classics

Seu George's covers of David Bowie. Also Butterfly Boucher's cover of Changes that Bowie liked so much he dubbed in additional vocals on it. 

The Under the Covers series by Susanna Hoffs and Dave Matthews.

There's always Bryan Ferry.

If you're interested in more traditional interpretations of the Broadway-Hollywood-Tin Pan Alley repertoire the various Smithsonian songwriter anthologies will lead you to singers you might thought of. Like for instance:

https://www.youtube.com/watch?v=nDKBOuvK8T8 

Matthew Sweet, Dave Matthews, whatever, he's obviously not the main attraction.

The fellow suggesting the full album cover of Dark Side of the Moon brings to mind Petra Haden singing ever vocal and instrumental part of The Who Sell Out. Petra Haden in general is someone to look into.