Of course Autumn Leaves is a standard (I have Grace Jones' campy, slightly off key disco version on vinyl). Eva's is brilliant. While a bit on the soft jazz side, I also love Dutch vocalist Laura Fygi's live version in French
http://www.youtube.com/watch?v=ZCToiC9GJsQ I *love* Laura Fygi's jazz take on Michel Legrand's I Will Wait for You from Umbrellas of Cherbourg, from her Legrand album he produced with her. For me, it's hands down the best take of the song in English--that ending wow.
http://www.youtube.com/watch?v=5OxEYNf1u3o It's impossible to beat the Dusty original (especially in the original Bacharach produced soundtrack version--the later single re-recording is a bit watered down), but I *love* The Zombies' take on The Look of Love done for BBC radio in the 60s. Colin Blunstone's vocals make me melt.
http://www.youtube.com/watch?v=r4emLYfb9rA Actually, I also love the jazzy cover of Summertime they do, though it's impossible to pick a favorite version of that song (I admit though, I've always found Joplin's overated *ducks*)
http://www.youtube.com/watch?v=Bo4cKTlGSFE (OK, I also love their cover of Will You Still Love Me Tomorrow? but I shouldn't turn this into a Zombies thread
http://www.youtube.com/watch?v=ftemreRiAzM )
Everyone here probably knows them, but as cheesy as they are (in a good way--at least for me), I think Donna Summer's disco takes on Barry Manilow's Could it Be Magic and Richard Harris' MacArthur Park crap all over the originals.
I suppose some of this depends on your definition of standards, but it seems like much from the early 70s or before counts now...