THIS is a topic!!
there's so many album songs i have fallen in love with that never saw the light of day, i will go through artist by artist

.
Firstly, my all time favourite artist
Madonna.
The First Album-Physical Attraction,I Know It and Think Of Me
Like A Virgin-Shoo-Bee-Doo,Stay and Pretender.
True Blue-Where's The Party
You Can Dance-Spotlight!
Like A Prayer-Love Song,Til' Death Do Us Part,Promise To Try,(unreleased in UK) Keep It Together and Pray For Spanish Eyes.
Erotica-Waiting,Words,Thief Of Hearts,Why's It So Hard,In This Life and Secret Garden.
Bedtime Stories-Forbidden Love and Sanctuary.
Ray Of Light-Swim,Sky Fits Heaven,Shanti/Ashtangi,Candy Perfume Girl,Skin and Mer Girl.
Music-Impressive Instant,Runaway Lover,Paradise(Not For Me) and Amazing
American Life-Intervention,Easy Ride,Mother & Father and (unreleased in UK) Nothing Fails.
Confessions On A Dance Floor-Future lovers,Let It Will Be,Forbidden Love,Isaac,Push,How High and Like it Or Not.
Hard Candy-Beat Goes on,Devil Wouldn't Recognize You,She's Not Me,Incredible and Heartbeat.
Britney Spears -
...Baby One More Time!-I Will Be There,Soda pop,Beat Goes On and I Will Still Love You
Oops!...I Did It Again-Satisfaction,What U See Is What U Get and Can't make you Love Me.
Britney-Cinderella,Let Me Be,Bombastic Love,Lonely,What It's like To Be Me and Before the Goodbye.
In the Zone-Showdown,Early Mornin',Shadow,Breathe On Me,Touch Of My Hand and Brave New Girl.
Blackout-Toy Soldier,Get Naked,Hot As Ice,Ooh Ooh Baby,Heaven On Earth,Freakshow and Perfect Lover.
Circus-Kill The lights,Shattered Glass,Unusual You and Blur.
Rihanna-
Good Girl Gone Bad-Good Girl Gone Bad,Sell Me Candy and Breakin' Dishes.
Rated R-Fire Bomb,Cold Case Love,The Last Song,Photographs and G4L.
Marvin Gaye-
What's Going On-What's Happening Brother,Flyin' High,Right on,Wholy Holy.
Let's Get It On-Please Stay,Keep Gettin' It On and Distant Lover.
Florence & The Machine-
Lungs- Howl,I'm Not Calling you A Liar, Between Two Lungs,My Boy Builds Coffins and Hurricane Drunk.
No Doubt/Gwen Stefani-
Tragic Kingdom-Happy Now?,Different people,The Climb,You Can Do It, End It On This,Sixteen and Tragic Kingdom.
Rock Steady-Making Out,Detective,Don't Let Me Down,Start The Fire,In My Head and Rock Steady.
L.A.M.B-The Real Thing,(unreleased in UK) Crash, and Danger Zone (most of album was released).
The Sweet Escape-Fluorescent,Don't Get It Twisted and Wonderful Life.
Christina Aguilera-
Stripped-Infatuation,Underappreciated,Make over,Cruz,Soar, and I'm OK.
Back To Basics-Makes Me Wanna Pray,Back In The Day,Oh Mother,On Our Way,Still Dirrty,Here To Stay,Welcome,Nasty Naughty Boy,I Got Trouble,Mercy On Me and The Right Man.
Bionic-(new but ones i love unreleased!). Bionic,Glam,Elastic Love,Prima Donna,WOOHOO,Lift Me Up,I Am,Vanity,Monday Morning,Birds Of Prey and Stronger Than Ever.
those are a grande selection THUS far! as loads of albums are recent and i don't know what will be released from them yet.