Carly Simon did a whole album of songs, appropriately titled “Torch.” With the cuts: “Blue of Blue,” “I’ll Be Around,” “I Got It Bad (And That Ain’t Good),” “Body and Soul,” “Not A Day Goes By,” and more.
For a more modern version, try “Love Stinks.” By Adam Sandler. (From “The Wedding Singer” a pretty good movie, with Drew Barrymore, yet).
I disagree with the OP, to an extent. A torch song is as much a style as it is content. Dramatic, long notes in there somewhere — “Every Day a Little Death” from A Little Night Music meets the OP definition, but it is not a torch song. On the other hand, you should put “Send In the Clowns” on your list. Definitely.
It doesn’t have to be lovers. “If He Walked Into My Life” from Mame is on the list, sung by an aunt to her nephew.
Others: “Sometimes Your Eyes Look Blue” and “Wanting Things”, from Promises, Promises.
“I Don’t Know How to Love Him”. Classic.
“You’re So Vain”, by Carly Simon. Bitter, a bit to much pop perhaps, but still in the range. “I had some dreams, they were clouds in my coffee.”
Bumbazine,
Heh! I guess you now know how old I am that I still call 'em “albums”! 
Brynda,
I’m not familiar with Diane Schuur. I’ll have to take a listen to some of her stuff.
Since Eve’s not around to do it, let me recommend Ute Lemper, the hottest thing to come out of Germany since the Luftwaffe.
Her BERLIN CABARET SONGS (available in both English and German versions on London’s Entartetmusik label, “Music Suppressed by the Third Reich”), are stunning versions of old Wiemar nightclub standards, hair-raising ballads of sexual deviance that’d have Marlene Dietrich blushing.
She’s also done a SINGS KURT WEILL, plus another album with the SEVEN DEADLY SINS and the MAHAGONNY Songspiel.
Or for something less twangy - Ingenue and Drag. Her latest release of ‘live’ tracks is also worth a listen, especially her rendition of Roy Orbison’s ‘Crying’.
Not to mention a number of other beautiful albums, like Just an illusion and City of strangers, and more recently Punishing kiss.
Yeah, but I hate PUNISHING KISS. Couldn’t listen to it all the way through. I’m only recommending the ones I liked.
What’ll I do? - Written by Irving Berlin, but effective when sung by any woman with a deep throaty voice a la Bea Arthur
Adia - Sarah McLachlan
Total Eclpise of the Heart - Bonnie Tyler
Unbreak My Heart - Tony Braxton
Nothing Compares to You - Sinead O’Connor
Always On My Mind - Willie Nelson
Heavan Knows - The Coors
And under the category of Big Hair Music:
I’ll Never Love This Way Again - Written (but peferrably not sung) by Barry Manilow
Ain’t No Mountain High Enough - Diana Ross
Remember Me - Diana Ross
Touch Me In The Morning - Diana Ross
Blue Bayou - Linda Rondstat
Whoa, this is old…
Okay, I thought of another one, though.
Crazy-Patsy Cline
This isn’t a torch song, but it’s definitely about loss. I Grieve, by Peter Gabriel. If that doesn’t match a sad mood, nothing will.
Company, written and performed by Rickie Lee Jones on her self-titled debut album.
Two words: Rosemary Clooney. One of the great torch song artists.
Try Blue Rose (1956), her great collaboration with Duke Ellington, or Love (1963), her collaboration with Nelson Riddle (who, incidentally, taught Linda Ronstadt a thing or two about torch songs, as romansperson has already acknowledged).
[hijack]
i don’t get this. isn’t cd the format, the album the collection of songs? why is a collection only an album if it appears on vinyl?
i call all lp length collections albums. if i say, ‘have you heard the new prodigy album?’, i’m not asking whether you’ve heard it on vinyl - isn’t the term not format exclusive? or have i been using it wrong?
[/hijack]
and i guess i’d better add some songs after my nasty hijack, so…
death cab for cutie - photo booth
the white stripes - i can’t wait
the smiths - there is a light that never goes out
the ataris - the last song i will ever write about a girl
the get up kids - out of reach
new found glory - hit or miss
Well, now that this has been revived:
Libby Holman’s Moanin’ Low, Why Was I Born? and There Ain’t No Sweet Man That’s Worth the Salt of My Tears
Alice Faye’s You’ll Never Know
Ruth Etting’s Mean to Me and Love Me or Leave Me
Julie London’s Cry Me a River
Attrayant and pesch, nice picks.
More Carly Simon: “Film Noir”, “Better Not Tell Her”, “It Should Have Been Me”
More Sarah McLachlan: “Possession”, “Terms (The Path of Thorns)”, “Vox”
More from the Corrs: “Closer”
Opal’s Greatest Karaoke Hits: The Sing-Along Sessions 
Abba: “The Winner Takes It All” – the ultimate in torch: written by the singer’s ex-husband, who divorced her.
Styx: “Love At First Sight”
Heart: “What About Love”, “Alone”, “Stranded”, “The Will to Love”, “Desire Walks On” (torch wailers, we might call them)
Roxette: “It Must Have Been Love”, “Spending My Time”
BBMak: “The Ghost of You and Me”
Jann Arden: “Cherry Popsicle”
Luba: “Everytime I See Your Picture”
Gloria Estefan: “Steal Your Heart”
38 Special: “Second Chance”
Fleetwood Mac: “In the Back of My Mind”, “Bleed to Love Her”
Judy Henkse. “'Til The Real Thing Comes Along.”
That lady can grab your heart and stomp on it with her voice.
May I heartily recommend you check out the work of Linda Eder, who is moderately famous but not nearly as much as she deserves to be. The woman has the finest singing voice and technique I’ve ever heard. Plenty of torch songs to enjoy, with ‘I’ll Forget You’, ‘When I Look At You’ and ‘Someone Like You’ among her finest moments. Utterly heart-wrenching, poignant, stirring, dramatic and evocative of emotions we’ve all felt at some time or other, delivered to the very peak of perfection.
Queen - "My Melancholy Blues"
She’s Gone - Hall and Oates
Invitation To The Blues - Holly Cole.
Actually, almost anything off of Temptation, Holly Cole’s 1995 album of all Tom Waits songs. She’s got a gorgeous voice and style.