The following is a complete (to my knowledge) set list for the Woodstock festival, held August 15-18, 1969. Four official various artists collections of Woodstock material have been released, each containing some tunes not available elsewhere:
Woodstock (1970, 3LPs)
Woodstock II (1971, 2LPs)
Woodstock - Three Days of Peace & Music: The 25th Anniversary Collection (1994, 4 CD boxed set)
Woodstock Diary (1994, 1 CD- intended as a sampler for the boxed set, it includes 5 songs not available elsewhere)

To date, only Jimi Hendrix' and Ravi Shankar's complete Woodstock sets have been issued seperately (although the Shankar set is missing one song). Many other acts have issued some songs from the festival on boxed sets and compilations; these are included in the "other" column. Although bootlegs are not counted on this page, I know the following artists' sets are easy to find on "underground" recordings: Janis Joplin, Grateful Dead, The Who, The Band, Crosby, Stills, Nash and Young.
I am trying to compile a complete set of the Woodstock material for a radio show on its 35th anniversary. Any help in obtaining material is appreciated!

There is a great site about the festival here.
Italicized information is unconfirmed.

Woodstock I Woodstock II boxed set Diary other
Richie Havens  High Flyin' Bird 
I Can't Make It Anymore  x
With A Little Help From My Friends 
Strawberry Fields For Ever 
Hey Jude 
I Had A Woman 
Handsome Johnny  x
Freedom  x x
Country Joe McDonald  I Find Myself Missing You 
Rockin' All Around The World 
Flyin' High All Over The World 
Seen A Rocket 
Fish Cheer/I-Feel-Like-I'm-Fixing-To-Die-Rag  x x
John B. Sebastian  How Have You Been 
Rainbows All Over Your Blues  x x
I Had A Dream  x x
Darlin' Be Home Soon 
Younger Generation 
Incredible String Band  Catty Come 
This Moment Is Different 
When You Find Out Who You Are 
Sweetwater  Motherless Child 
Look Out 
For Pete's Sake 
Day Song 
What's Wrong  x
Crystal Spider 
Two Worlds 
Why Oh Why 
Bert Sommer  Jennifer 
America 
Tim Hardin  If I Were A Carpenter  x x
Ravi Shankar  Raga Puriya-Dhanashri/Gat In Sawarital  x
Tabla Solo In Jhaptal  x
Raga Manj Kmahaj  x
Alap Jor 
Dhun In Kaharwa Tal  x
Medium & Fast Gat In Teental  x
Melanie  Beautiful People  x x
Birthday Of The Sun  x
Arlo Guthrie  Coming Into Los Angeles  x x
Walking Down The Line  x
Amazing Grace 
Joan Baez  Joe Hill  x x
Sweet Sir Galahad  x x
Drug Store Truck Driving Man  x x
Swing Low Sweet Chariot 
We Shall Overcome 
Quill  Waitin' For You 
Keef Hartley  ?
Santana  Persuasion  x
Soul Sacrifice  x x
Savor x
Fried Neck Bones x
Canned Heat  A Change Is Gonna Come
Leaving This Town  x
Woodstock Boogie  x
Going Up The Country  x x
Let's Work Together 
Too Many Drivers At The Wheel 
Mountain  Blood Of The Sun (3:05) B (3:31)  x x
Stormy Monday 
Long Red 
For Yasgur's Farm 
Theme From An Imaginary Western  x x
Waiting To Take You Away 
Dreams Of Milk And Honey 
Blind Man 
Blue Suede Shoes 
Southbound Train  x
Janis Joplin  Raise Your Hand 
As Good As You've Been To This World 
To Love Somebody 
Summer-time  x
Try (Just A Little Bit Harder)  x x
Kosmic Blues 
Can't Turn You Loose 
Work Me Lord  x
Piece Of My Heart  x
Ball and Chain  x x
Sly & The Family Stone  Love City  x
Dance To The Music  x x
Music Lover x x
I Want To Take You Higher  x ?
Grateful Dead  St. Stephen 
Mama Tried 
Dark Star/High Time 
Turn On Your Lovelight 
CCR Born On The Bayou 
Green River  x
Ninety-Nine And A Half (Won't Do)  x
Commotion  x
Bootleg 
Bad Moon Rising 
Proud Mary 
I Put A Spell On You  x
Night Time Is The Right Time 
Keep On Choogin' 
Suzy Q 
The Who  Heaven And Hell 
I Can't Explain 
It's A Boy 
1921
Amazing Journey 
Sparks  x
Eyesight To The Blind 
Cristmas 
Tommie Can You Hear Me 
Acid Queen  x
Pinball Wizard  x
Abbie Hoffmann Incident  x
Fiddle About 
There's A Doctor I've Found 
Go To The Mirror Boy 
Smash The Mirror 
I'm Free 
Tommy's Holiday Camp 
We're Not Gonna Take It  x x
See Me Feel Me 
Summertime Blues 
Shakin' All Over 
My Generation 
Naked Eye 
Jefferson Airplane  The Other Side Of This Life 
Plastic Fantastic Lover  x
Volunteers  x x
Saturday Afternoon/Won't You Try  x x
Eskimo Blue Day  x
Uncle Sam's Blues  x
Somebody To Love  x x
White Rabbit  x x
Joe Cocker  Delta Lady 
Some Things Goin' On 
Let's Go Get Stoned  x x
I Shall Be Released  x
With A Little Help From My Friends  x x
Country Joe & The Fish  Barry's Caviar Dream 
Not So Sweet Martha Lorraine 
Rock And Soul Music  x x
Thing Called Love 
Love Machine 
Fish Cheer/I-Feel-Like-I'm-Fixing-To-Die-Rag  x x
Ten Years After  Good Morning Little Schoolgirl 
I Can't Keep From Crying Sometimes 
I May Be Wrong, But I Won't Be Wrong Always 
I'm Going Home  x x
The Band  Chest Fever 
Baby Don't Do It 
Tears Of Rage 
We Can Talk 
Long Black Veil  x
Don't You Tell Henry 
Ain't No More Cane  x
Wheels On Fire 
Loving You Is Sweeter Than Ever  x
The Weight  x
BS&T More And More 
I Love You Baby More Than You Ever Know 
Spinning Wheel 
I Stand Accused 
Something Coming On 
Johnny Winter  Mean Town Blues  x x
CSN&Y Suite Judy Blue Eyes  x x
Blackbird  x
Guinnevere  x x
Marrakesh Express  x x
4 + 20  x x
Mr Soul 
Sea Of Madness  x x
Wooden Ships  x
Find The Cost Of Freedom  x
Paul Butterfield Blues Band  Everything's Gonna Be Alright  x
Driftin' 
Born Under A Bad Sign 
All My Love Comin' Through To You 
Love March  x x
Sha-Na-Na  Na Na Theme 
Jakety Jak 
Teen Angel 
Jailhouse Rock 
Wipe Out 
Who Wrote The Book Of Love 
Duke Of Earl 
At The Hop  x x
Na Na Theme 
Jimi Hendrix  Message To Love  x
Getting My Heart Back Together Again  x x
Spanish Castle Magic  x
Red House  x
Master Mind  x
Here Comes Your Lover Man  x
Foxy Lady  x
Beginning  x
Izabella  x x
Gypsy Woman  x
Fire  x
Voodoo Child (slight return)/Stepping Stone  x x x
Star Spangled Banner  x x x
Purple Haze  x x x
Woodstock Improvisation  x x
Villanova Junction  x
Hey Joe x
Woodstock I Woodstock II boxed set Diary other