(I offer these with the caveat that some of the songs may sound a particular way - sad or happy for example - until you listen to the words. A sad song set to peppy music depresses me more sometimes than that sounds as moreose as its lyrics.)
Wallowing Music:
Tracy Chapman's "Fast Car" is IMHO the saddest song written in the past twenty years. On the other hand, most of her other stuff is great for any sort of introspective mood you might be in.
Dire Straits "Romeo and Juliet" runs a close second, though its a bit less sad, and a bit more angry. For a more obviously bitter and angry version, try the Indigo Girls' cover, but the DS original is, IMO, superior.
Paul Simon had wrote some excellent, but very depressing, music around the time of his first divorce. See especially "Hearts and Bones" and "Train in the distance"
Janis Joplin is usually great for when I'm low. "Me and Bobby McGee," especially.
Steely Dan's "Deacon Blues" and "Hey Nineteen" are jazz/rock, if you're looking for something that's cool and depressing at the same time.
Bill Withers "Ain't No Sunshine" was IMHO the best song to come out of the 1970's
Some of Billy Joel's stuff is really worth a listen. "Scene's from an Italian Restaurant," "Captain Jack," "Allentown" and the more recent "Downeaster Alexa" are all depressing as hell.
John Lee Hooker is my favorite blues artist, and "One Bourbon, One Scotch, One Beer," "Bang, Bang, Bang, Bang," "Think Twice Before You Go" and most anything else is great wallowing music.
My wallowing music of choice in high school was just about anything by Pink Floyd. The Grateful Dead were pretty good, too. Except for the Dead's "Mexicali Blues" which I play a lot, I've sort of listened to these albums too much for them to turn to these days.
I know you said country didn't ususally do much for you, but old school country is pretty diffreent from newer stuff, so I'll include only a couple of my favorites on the chance that you're less familiar with the old stuff.
Willie Nelson: "Blue Eyes Crying in the Rain," "Crazy" (Can't go wrong with Patsy Cline version of this either), "City of New Orleans" (Which sounds all happy go luck, until you realize its all about loss), and his version of "Georgia on My Mind." I could go on, but won't for now.
Patsy Cline: The aforementioned "Crazy," and "I Fall to Pieces"
Pull yourself out of it kind of music:
Not too many common threads here, except for maybe a number of songs featuring driving guitar.
Eric Clapton songs usually fall into the latter category. "Layla," for example. Of course, I porabably should have listed "Promises" in the Wallowing section.
Alanis Morisette's "Jagged Little Pill" usually lifts my mood but "You Oughta Know" always makes me want to run and hide.
Dire Straits "Sultans of Swing," "Walk of Life," and others are great for improving my outlook.
Crosby, Stills, and Nash's music is fabulous and musically intelligent. Their greatest hits album, though it has some sad stuff on it, always ends up making me happy because it's just so incredible.
Ike and Tina Turners's "Proud Mary" is great, especiialy after your mood improves a bit. Especially if you happen to be a bit (more than a bit?) tipsy (and are over legal age, yada yada) and end up dancing around your apartment to it.
More Bill Withers (a terribly underappreciated artist): "When I'm Kissing My Love" and "Lovely Day" and "Just the Two of Us."
"Grandma's Hands" makes me cry, but in a happy way. I couldn't put it in the other section.
Stevie Wonder is great - "For Once in My Life" for example.
No Doubt's "I'm Just a Girl" and "Spiderweb" and others were played a lot at the gym I used to attend, and working out always makes me feel better. I, therefore, associate these songs with feeling better. YMMV.
Bob Marley's music is often hopeful even when its sad, and it usually improves my mood. "Every Little THing is Going to Be Alright" especially.
Again with the country:
Johnny Cash: "A Boy Named Sue"
Chalie Daniels: "The Devil Went Down to Georgia"
Johnny Horton: "May the Bird of Paradise Fly Up Your Nose"
I guess that's enough for now. Edit: I had left out Bill Withers, which I just couldn't do.