I'm with Ella about Peggy Lee, but prefer her rendering of 'Fever'. Another that sticks in my mind is 'Miss Otis Regrets', preferably the Ella Fitzgerald version.
The Stereophonics also do a nice version of Handbags and Gladrags. My favourite is Cathy’s Clown by The Everly Brothers, it always reminds me of the year I left school and I equally love A Different Corner by George Michael. DH’s favourites are The First Time Ever I Saw Your Face by Roberta Flack and ‘Bring Him Home’ by Il Divo. Last Christmas I bought DH the CD of Roy Orbison with The Royal Philharmonic Orchestra. The first track is In Dreams and it made us both cry so that is becoming a favourite too. Sorry I know it should be one but it’s too hard to choose one.