Wynbish, I think you and I have similar tastes in vocalists, because Madeleine Peyroux and Ingrid Michaelson are excellent choices.
To add to Madeleine Peyroux, I love her cover of "Dance Me To the End of Love" (not sure if that really counts as a standard): http://www.youtube.com/watch?v=AqpOFQvMM1A
Belle Linda Halpern sang a version of "Lost in the Stars" at a friend's memorial service in the early '90s and just typing the phrase "Belle Linda Halpern sang a version of 'Lost in the Stars'..." gave me goosebumps and brought tears to my eyes. I hadn't forgotten all about it until I saw this thread. I don't see a version of it online anywhere (the Phranc song either), but I did find a recording of "If I Can Dream," made famous by the Elvis. Belle Linda Halpern
Javero, I always assumed Julie London's Cry me a River *was* the first major released version. It's the one I always go to, and an absolute fave of mine (there was a 90s version I kinda liked by UK one hit wonder JAI, who had a big hit here with I Believe. It sounds kinda dated now with its commercialized take on Portishead production, but I still kinda like it http://www.youtube.com/watch?v=oH86E17fNrk ).
*edited* I guess nobody ever said that you couldn't choose the first version of a song as the fave--I misread the question. Julie's Cry Me a River was the first one released, accoring to Wiki but it was written first for Ella, but she didn't end up recording it till 6 years after Julie.
Michelle, you along with a few others will probably change your opinion of me after I reveal that neither the voice of Sinatra nor Ella nor Streisand nor Diahann Carroll ever did anything for me.
For me, among the great crooners of the past Perry Como reined supreme followed closely by Vic Damone, Andy Williams and Nat King Cole . My starting lineup on the distaff side is made up Julie London, Sarah Vaughan, Dusty Springfield, Dame Shirley Bassey and Dionne Warwick (before too many Newport Menthols).
Dionne Warwick is my favorite 60s vocalist--aside from so many great singles, all of her albums with Bacharach as arranger are pretty great. I admit, it was thrilling to finally see her live, but it's so utterly ridiculous how she still proclaims at every chance she has, with no sense of irony, that her smoking has never remotely affected her voice, and if it ever started to she would stop immediately. Of course voices often change with age--but her range and delivery in the 60s and into the 70s was, IMHO honestly up there with the greats like Ella--20 years later, the range anyway was largely gone.
Speaking of Dionne, two of her covers of Leslie Bricusse and Anthony Newley standards recorded in 1965 that I love, both arranged and conducted by Burt Bacharach.
And somewhat different, and while nothing can replace Nina Simone's definitive take on Bricusse/Newley's Feeling Good, I admit, I *love* Muse's cover: http://www.youtube.com/watch?v=CmwRQqJsegw
"The gods who nurse this universe think little of mortals' cares. They sit in crowds on exclusive clouds and laugh at our love affairs. I might have had a real romance if they'd given me a chance. I loved him, but he didn't love me. I wanted him, but he didn't want me. Then the gods had a spree and indulged in another whim. Now he loves me, but I don't love him." - Cole Porter
"The gods who nurse this universe think little of mortals' cares. They sit in crowds on exclusive clouds and laugh at our love affairs. I might have had a real romance if they'd given me a chance. I loved him, but he didn't love me. I wanted him, but he didn't want me. Then the gods had a spree and indulged in another whim. Now he loves me, but I don't love him." - Cole Porter