They have to fit on 2 cd's and you can only use stuff already released on official cd's.
Here's my picks (all are Album Versions unless specified otherwise):

Essential 1
1. Controversy
2. 1999
3. Little Red Corvette
4. When Doves Cry
5. Let's Go Crazy (Special Dance Mix)
6. Erotic City (Edit)
7. The Beautiful Ones
8. Computer Blue
9. Purple Rain
10. Raspberry Beret (Extended Remix)
11. A Love Bizzare (Edit)
12. Kiss (Extended Remix)
13. Girls and Boys

Essential 2
1. Sign 'O' the Times
2. Housequake
3. The Ballad of Dorthy Parker
4. Forever in My Life
5. U Got the Look (Long Look)
6. If I Was Your Girlfriend
7. I Could Never Take the Place of Your Man
8. Alphabet Street
9. Gett Off
10. Cream
11. Diamonds and Pearls
12. Sexy MF
13. 7
14. Empty Room
15. Musicology
16. Guitar

well with very few changes to your list a few additions and subtractions you have Prince Ultimate. Not a very good "essential" list especially since it's mostly common pop tracks. You should find some of them rare jems that make it essential for a prince "first time listener" to hear. I think essential means if U never really listened to prince other than the usual hits, U must essentially check out these tracks..... know what i'm saying?
[Edited 3/26/09 6:43am]

My Dream Set.....

Ultimate 2

Disc 1

I Feel For You
Dirty Mind
When You Were Mine
Gotta Broken Heart Again
Baby Im A Star
The Beautiful One's
Paisley Park
Sometimes It Snows In April
Play In The Sunshine
Housequake
Starfish and Coffee
Adore
Space
The Most Beautiful Girl In The World
White Mansion
Face Down

Disc 2

God
God (instrumental)
4 The Tears In Your Eyes (studio version)
17 Days
Erotic City (extended version)
Another Lonley Christmas (exetended version)
How Come You Dont Call Me Anymore
Hello (extended version)
Space (Universal Love Remix)
So Far, So Pleased
Tangerine (Extended Version)
U Make My Sunshine
Song Of The Heart
[Edited 3/26/09 9:17am]

omnithanos said:

nah most of that list has been released before on "hits" collections of P's its time 2 make room for his more abscure tracks...which in my opinion are far better

The essential Prince has to include the protege music
so 4 me disc 1 would highlight the music that defines Prince's real art
that isn't regularly heard or played
disc 2 would highlight the best Prince's songs with/thru proteges

Disc 1
the Future
Positivity
Love or Money
Money Don't Matter 2night
I Wish U Heaven
God [the Dance Electric]
Power Fantastic
Everywhere
Erotic City
Free
America (full version or 8 minute cut)
Sexuality
Uptown
I Wonder U
Space
Condition of the Heart
Strange Relationship
Bob George
Strollin
Tangerine
Girl (extended version)
Rock Hard in a Funky Place
3121

Disc 2
Noon Rendezvous (Sheila E)
Yes (the Family)
777-9311 (the Time)
Stroke (Mazarati)
Cool (the Time)
Dear Michaelangelo (Sheila E)
Shortberry Strawcake (Sheila E)
Nasty Girls (Vanity 6)
If A Girl Answers Vanity 6)
I Guess It's All Over (Mazarati) http://www.myspace.com/100mhp
Jerk Out (the Time)
G-Spot (Jill Jones)
Screams of Passion (the Family)
Love on a Blue Train (Sheila E)
Susannah's Pajamas (the Family)
11 (Babydoll House) (Madhouse)
Mia Boca (Jill Jones)
Love Is Contagious (Taj Seville)
If The Kid Can't Make U Come (the Time)
I Don't Want 2 Leave U (the Time)

I don't think it's possible to do that in 2 discs....

I would not however have "Guitar" anywhere near an essential list...

I would have Endorphinemachine on there...Days o' Wild.....ummm Bat Dance (not a "real" song per se but essential none the less), Somebody's Somebody...just to name a few...

1st:

1. From The Lotus
2. Boom
3. Crimson & Clover
3. The Morning After
4. 4ever
5. Colonized Mind
6. Feel Good, Feel Better, Feel Wonderful
7. Love Like Jazz
8. 77 Beverly Park
9. Wall Of Berlin
10. $
11. Dreamer
12. Back To The Lotus

2nd:

1. There’ll Never B (Another Like Me)
2. Chocolate Box
3. Dance 4 Me
4. U’re Gonna C Me
5. Here
6. Valentina
7. Better With Time
8. Ol’ Skool Company
9. No More Candy 4 U

Dave1992 said:

lol I think u can only do an essentials disc after a certain amount of albums after that particular album

I see essentials disc for people who came with 2 albums lol

OldFriends4Sale said:

My answer was not the most serious of all.