Using songs from their entire discography. You can do this more than once, considering some of us have more than 1 favorite.
I'll start with Rihanna:
CD would be called "Questions Existing"
1. What's My Name
2. Unfaithful
3. G4L
4. Breakin Dishes
5. Rehab
6. Umbrella
7. We Ride
8. Only Girl (In The World)
9. S&M
10. Russian Roulette
11. Rude Boy
Break The Ice
Stronger
Freakshow
Rebellion
Everytime
Toxic
Gimme More
Piece of Me
I'm a Slave 4 You
Breathe on Me
Radar
Baby One More Time
Out of This World (Bonus)
Brave New Girl (Bonus)
1. Waiting For Tonight
2. Get Right
3. If You Had My Love
4. Love Don't Cost A Thing
5. Play
6. I'm Gonna Be Alright (feat. Nas)
7. Step Into My World
8. Too Late
9. Dance With Me
10. All I Have (feat. LL Cool J)
11. Forever
12. Open Off My Love
13. Brave
14. Waiting For Tonight (Hex Hector Remix)
Brandy has too many amazing songs. And no "The Boy Is Mine" will not be making an appearance on this album.
ARTIST: Brandy TITLE: Maximum Risk
1. Right Here (Departed)
2. Drum Life
3. Freedom
4. Gonna Find My Love
5. Home
6. WOW
7. Romeo & Juliet
8. Afrodisiac
9. Today
10. Stand Back
11. Lifeguard
12. A Capella (Something's Missing)
13. What About Us?
14. I Thought
15. Leave
16. Tomorrow
17. Surprise Ending
1. Umbrella (feat. Jay-z)
2. SOS
3. Breakin Dishes
4. Let Me
5. That La La La
6. S&M
7. If Its Lovin That You Want
8. Dont Stop The Music
9. Take A Bow
10. Pon De Replay
11. Lemme Get That
12. Russian Roulette
13. Unfaithful
14. Hard
15. Rude Boy
16. Whats My Name
17. Only Girl
18. Disturbia
1. Bad Romance
2. Poker Face
3. Just Dance
4. Paparazzi
5. Monster
6. Dance In The Dark
7. Paper Gangsta
8. Fooled Me Again
9. LoveGame
10. So Happy I Could Die
11. Telephone
12. Alejandro
1. Fallin
2. If I Aint Got You
3. Waiting For Your Love
4. Karma
5. Heartburn
6. How Come You Dont Call Me?
7. No One
8. Superwoman
9. Put It In A Love Song (feat. Beyonce)
10. Go Ahead
11. Like You'll Never See Me Again
12. Like the Sea
13. Love is My Disease
14. Empire State of Mind Part 2
15. Teenage Love Afair
16. Un-Thinkable
17. Try Sleeping With A Broken Heart
1. Lets Get It Started
2. I Gotta Feeling
3. Hey Mama
4. Boom Boom Pow
5. The Time (The Dirty Bit)
6. Shut Up
7. Pump It
8. My Humps
9. Electric City
10. Dum Diddly
11. Ring-a-Ling
12. Grapes
13. Third Eye
14. Ba Bump
15. Imma Be
1. What's My Name
2. Umbrella
3. Rude Boy
4. Russian Roulette
5. Firebomb
6. Only Girl (In The World)
7. Rehab
8. California King Bed
9. Shut Up and Drive
10. Hate That I Love You
11. Te Amo
12. S&M
13. Breakin Dishes (Bonus Track)
14. Don't Stop The Music (Itunes Bonus Track)
Considering there is room for 14 songs, this would be the order:
SHAKIRA Title: Instinct
1. La Tortura
2. Loca
3. Pies Descalzos, Sueños Blancos
4. Antes de las Seis
5. Despedida
6. Objection (Tango)
7. Whenever, Wherever
8. Men In This Town
9. Si Te Vas
10. She Wolf
11. Inevitable
12. Se Quiere, Se Mata
13. Illegal
14. Día de Enero
1. When You Were Young
2. Midnight Show
3. All These Things That I've Done
4. For Reasons Unknown
5. Joy Ride
6. Human
7. Tranquilize
8. Romeo and Juliet
9. Read My Mind
10. Bones
11. Bling (Confession of a King)
12. This River is Wild
13. Sam's Town
14. Mr. Brightside
1. My Heart
2. Where The Lines Overlap
3. Decoy
4. Careful
5. Stop This Song
6. Never Let This Go
7. Born For This
8. Misery Business
9. Fences
10. All We Know
11. Brighter
12. Misguided Ghosts
13. We Are Broken
14. All I Wanted
1. Bad Romance
2. Poker Face
3. Dance in the Dark
4. I Like It Rough
5. Money Honey
6. Paper Gangsta
7. Alejandro
8. Brown Eyes
9. Speechless
10. Telephone
11. LoveGame
12. Paparazzi
Fergie, Will.i.am and The Black Eyed Peas Title: The Wave
1. Hey Mama
2. Don't Phunk with My Heart
3. Heartbreaker
4. Glamorous
5. Don't Lie
6. Big Girls Don't Cry
7. Alive
8. Fergalicious
9. Pump It
10. Let's Get It Started
11. Shut Up
12. Where is the Love
13. Gone Going
14. Mary Jane Shoes
1. Boys
2. (You Drive Me) Crazy
3. Born To Make You Happy
4. ...Baby One More Time
5. Oops...I Did It Again
6. I'm A Slave 4 U
7. Toxic
8. Outrageous
9. Gimme More
10. Piece Of Me
11. Get Naked
12. Womanizer
13. Circus
14. If U Seek Amy
15. Unusual You
16. Hot As Ice
Bonus Tracks
1. Amnesia
2. Everytime
3. Like A Virgin (Cover)
1. Stranger
2. With Love
3. Fly
4. Come Clean
5. Wake Up
6. Outside of You
7. Beat of My Heart
8. Our Lips Are Sealed
9. Who's That Girl?
10. Where Did I Go Right?
11. Someone's Watching Over Me
12. Now You Know
13. What Dreams Are Made Of
14. Reach Out
1. Reb'l Fleur (New Track)
2. Only Girl
3. Whats My Name
4. S&M
5. Fading
6. Cheers
7. Te Amo
8. Fire Bomb
9. Rude Boy
10. Skin
11. Disturbia
12. The Last Song
1. Flaws and All
2. World Wide Woman
3. Listen
4. Me Myself and I
5. Irreplaceable
6. Halo
7. Satellites
8. Hello
9. Sweet Dreams
10. If I Were a Boy
11. If
12. Dangerously In Love
I WOULD BUY 2398 COPIES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. Paper Gangsta
2. Dance In The Dark
3. Money Honey
4. Just Dance
5. Second Time Around
6. Monster
7. Poker Face
8. Alejandro
9. So Happy I Could Die
10. Beautiful, Dirty, Rich
11. LoveGame
12. Bad Romance
13. Vanity
14. Paparazzi
15. Telephone (feat. Beyoncé)
16. Nothin On (But The Radio)
17. No Way (Bonus Track)
And no "The Boy Is Mine" will not be making an appearance on this album. 
