I heard her on cable music, and bought The Very Best of Diana Krall on Ebay.
I have described jazz to Mrs. Plant (v.3.0) as your heads are on the same pillow, and blues as moving away from each other on a train.
Ms. Krall is very good, I can best describe her voice and her style in cover songs as intimate. I particularly like her version of The Look of Love.
Do any Dopers have recommendations for her other albums?
I recommend Tierney Sutton, and Betty Carter over Diana Krall, easy. I find her a little too cold, and past expiration date with the tune choice. “Oh yeah I knew she was going to do that one” Even Lea Delaria, believe it or not is great. She does a version of “Sweeney Todd” that sounds like pure honey.
Whatever you do, don’t buy her Christmas album, called “Seasons”. It’s really, really NOT her forte. I like her, and I like Jane Monheit, and I’ve seen them both in concert. Seems like when they hit the big time, the hating starts, but I still like them both.
I am unlikely to buy anyone’s Christmas Album. 
Thanks for the recommendations, I shall try them.
I like Diana Krall quite a bit despite her limitations as a vocalist. Jane Monheit and Tierney Sutton are, without doubt, better singers. However, Diana’s true strengths are her excellent piano playing and talent as a band leader. Unfortunately, that tends to get overlooked, especially in mainstream media coverage.
To get a better idea of her musicianship, definitely pick up “Live in Paris”. I think she really shines on this CD. My other favourites include “All For You: A Tribute to Nat King Cole”, “Love Scenes” and the more recent album of 20’s and 30’s tin pan alley songs “Glad Rag Doll”.
She may be the hottest 50 yr old ever.
She’s a good mood singer but can really kick butt when she wants to. I particularly like her way with Diana Krall - Frim Fram Sauce (Live)
She’s great live, I saw her at Tanglewood several summers ago. I definitely second the recommendation of Live in Paris.
When I Look in Your Eyes is the best of her studio albums, IMO. I also particularly liked Quiet Nights from 2009.
I’d also like to say to Canada that Diana Krall almost makes up for Celine Dion.
If you find yourself liking female vocal jazz, branch out a bit. I find Ms. Krall to be impossibly derivative (of Nat King Cole, mainly), and I think she has traded on her looks quite a bit. There are tons and tons of great vocalists to choose from–my all time faves are Abbey Lincoln and Anita O’ Day, but besides the ones already mentioned, there are so many others out there, from bluesy and sassy (Etta Jones, Carmen McRae) to sultry (June Christie) to whimsical (Blossom Dearie), just off the top of my head. Oh man, so many to enjoy.
Well sure, but they’re all dead. Krall does just fine in keeping the American Songbook alive and well. Other contemporary singers that rate very highly are Karrin Allyson, Madeleine Peyroux, Cassandra Wilson, Lani Hall, and Dianne Reeves.
Well said. In the Nat King Cole bag I particularly like Diana Krall - You’re Looking at Me – written by MR Julie London! 
(who also gave us Route 66.)
Mr Julie London? Can’t you give a composer some credit?
I assume you meant Bobby Troup?
There’s certain vulnerability and passion missing in Diana to me. Jazz is improvisational and she sounds facile.
I heard her on the cable music jazz channel, and bought the CD without knowing what she looked like. 
Well, they can’t all be Ella Fitzgerald.
Dude, I dare you to listen to Lea Delaria doing “Sweeney Todd.” I Posted it above. I vouch it’ll groove you no end.
Yes. A cool guy whose being husband to one of the foxiest singers ever was at least as big a deal as his other accomplishments – at least to me.
As you probably know he was husband-in-law to Jack Webb.