I did not have a lot of time to find a lot of good songs outside of the albums above, but here's a few great ones (in the wrong order probably, I'm bad at ranking):
1 | Albert Ayler | "Ghosts"
2 | Nina Simone | "Sinnerman"
3 | Bob Dylan | "Desolation Row"
4 | John Coltrane | "A Love Supreme, Part I: Acknowledgement"
5 | Bobby Hutcherson | "Dialogue"
6 | Bob Dylan | "Mr. Tambourine Man"
7 | The Albert Mangelsdorff Quintet | "Es sungen drei Engel"
8 | Simon & Garfunkel | "The Sound of Silence"
9 | Ahmad Jamal | "Extensions"
10 | Anthony Williams | "Memory"
11 | Niels Viggo Bentzon | "Walking Monkey"
12 | Ornette Coleman | "Dedication to Poets and Writers"
13 | György Ligeti | "Requiem"
14 | Bob Dylan | "Positively 4th Street"
15 | Steve Reich | "It's Gonna Rain, Part I"
16 | Barry McGuire | "Eve of Destruction"
17 | Nina Simone | "Feeling Good"
18 | Stan Tracey | "Starless and Bible Black"
19 | Bobby Hutcherson | "Les Noirs Marchant"
20 | Sonny Simmons, Clifford Jordan, Prince Lasha & The Bossa Três | "Blue Monk"
21 | John Coltrane | "A Love Supreme, Part IV: Psalm"
22 | Bob Dylan | "Like a Rolling Stone"
23 | Son House | "Grinnin' in Your Face"
24 | Bob Dylan | "It's Alright, Ma (I'm Only Bleeding)"
25 | The Horace Silver Quintet | "The Kicker"
26 | Niels Viggo Bentzon | "In the Old Candy Store"
27 | Albert Ayler Trio | "Spirits"
28 | The Albert Mangelsdorff Quintet | "Sakura Waltz"
29 | Anthony Williams | "Two Pieces of One: Green"
30 | Mimi & Richard Farina | "Reno Nevada"
31 | Ornette Coleman | "Sadness"
32 | Nina Simone | "Strange Fruit"
33 | Bob Dylan | "Ballad of a Thin Man"
34 | Pete La Roca | "Malaguena"
35 | The Beach Boys | "Barbara Ann"
36 | The Albert Mangelsdorff Quintet | "Raknash"
37 | Moacir Santos | "Coisa N°2"
38 | Ahmad Jamal | "Whisper Not"
39 | Sambrasa Trio | "Aleluia"
40 | The Beatles | "Yesterday"
41 | Bob Dylan | "Subterranean Homesick Blues"
42 | The Albert Mangelsdorff Quintet | "Now Jazz Ramwong"
43 | Grachan Moncur III | "Nomadic"
44 | The Horace Silver Quintet | "Song for My Father"
45 | The Beatles | "Run for Your Life"
46 | Sandy Bull | "Blend II"
47 | Anthony Williams | "Two Pieces of One: Red"
48 | Davy Graham | "Moanin'"
49 | Bobby Hutcherson | "Catta"
50 | The Byrds | "Mr. Tambourine Man"
The entire shortlist:
Herb Alpert & The Tijuana Brass | A Taste of Honey
Albert Ayler Quartet | Ghosts
Albert Ayler Quartet | Holy Spirit
Albert Ayler Quartet | Mothers
Albert Ayler Trio | Ghosts: First Variation
Albert Ayler Trio | Ghosts: Second Variation
Albert Ayler Trio | Spirits
Charles Aznavour | La bohème
The Beach Boys | Barbara Ann
The Beatles | Help!
The Beatles | In My Life
The Beatles | Norwegian Wood (This Bird Has Flown)
The Beatles | Nowhere Man
The Beatles | Run for Your Life
The Beatles | Ticket to Ride
The Beatles | We Can Work It Out
The Beatles | Yesterday
Niels Viggo Bentzon | In the Old CandyStore
Niels Viggo Bentzon | No Style
Niels Viggo Bentzon | Nylon Tip
Niels Viggo Bentzon | Walking Monkey
Art Blakey & The Jazz Messengers | The Core
Art Blakey & The Jazz Messengers | Free for All
Art Blakey & The Jazz Messengers | Hammer Head
Sandy Bull | Blend II
Sandy Bull | Manha de Carnival
Sandy Bull | Memphis, Tennessee
The Byrds | Mr. Tambourine Man
The Byrds | Turn! Turn! Turn! (To Everything There Is a Season)
Martin Carthy | Scarborough Fair
Ornette Coleman | The Ark
Ornette Coleman | Dedication to Poets and Writers
Ornette Coleman | Doughnut
Ornette Coleman | Sadness
John Coltrane | A Love Supreme, Part I: Acknowledgement
John Coltrane | A Love Supreme, Part II: Resolution
John Coltrane | A Love Supreme, Part III: Pursuance
John Coltrane | A Love Supreme, Part IV: Psalm
The John Coltrane Quartet | Song of Praise
Country Joe & The Fish | I-Feel-Like-I‘m-Fixin‘-to-Die-Rag
Miles Davis | Agitation
Miles Davis | E.S.P.
Miles Davis | Eighty-One
The Dixie Cups | Iko Iko
Bob Dylan | Ballad of a Thin Man
Bob Dylan | Desolation Row
Bob Dylan | Gates of Eden
Bob Dylan | Highway 61 Revisited
Bob Dylan | It Takes a Lot to Laugh, It Takes a Train to Cry
Bob Dylan | It‘s All Over Now, Baby Blue
Bob Dylan | It‘s Alright, Ma (I‘m Only Bleeding)
Bob Dylan | Like a Rolling Stone
Bob Dylan | Mr. Tambourine Man
Bob Dylan | Positively 4th Street
Bob Dylan | Queen Jane Approximately
Bob Dylan | Subterranean Homesick Blues
Bob Dylan | Tombstone Blues
Booker Ervin | Number Two
Mimi & Richard Farina | Reno Nevada
Jackson C. Frank | Just Like Anything
Jackson C. Frank | Kimbie
Jackson C. Frank | Milk and Honey
Jackson C. Frank | My Name Is Carnival
Jackson C. Frank | You Never Wanted Me
Dexter Gordon | Tanya
Davy Graham | Maajun (A Taste of Tangier)
Davy Graham | Moanin‘
Grant Green | Nomad
Joe Henderson | Short Story
Andrew Hill | Refuge
Son House | Grinnin‘ in Your Face
Son House | John the Revelator
Son House | Louise McGhee
Bobby Hutcherson | Catta
Bobby Hutcherson | Dialogue
Bobby Hutcherson | Ghetto Lights
Bobby Hutcherson | Idle While
Bobby Hutcherson | Les Noirs Marchant
The Impressions | People Get Ready
Ahmad Jamal | Extensions
Ahmad Jamal | This Terrible Planet
Ahmad Jamal | Whisper Not
Bert Jansch | I Have No Time
Bert Jansch | Needle of Death
Bert Jansch | Running from Home
B.B. King | How Blue Can You Get
B.B. King | Worry, Worry
Roland Kirk | The Business Ain‘t Nothin‘ But the Blues
The Roland Kirk Quartet | Mystical Dream
The Roland Kirk Quartet | Once in a While
Pete La Roca | Basra
Pete La Roca | Candu
Pete La Roca | Malaguena
Pete La Roca | Tears Come from Heaven
The Mamas & The Papas | California Dreamin‘
The Albert Mangelsdorff Quintet | Blue Fanfare
The Albert Mangelsdorff Quintet | Es sungen drei Engel
The Albert Mangelsdorff Quintet | Now Jazz Ramwog
The Albert Mangelsdorff Quintet | Raknash
The Albert Mangelsdorff Quintet | Sakura Waltz
The Albert Mangelsdorff Quintet | Three Jazz Moods
Barry McGuire | Eve of Destruction
Grachan Moncur III | Nomadic
Grachan Moncur III | The Twins
Thelonious Monk | Children‘s Song (That Old Man)
Ennio Morricone | Per Qualche Dollaro in Più [For a Few Dollars More] (Main Theme)
Otis Redding | My Girl
Steve Reich | It‘s Gonna Rain, Part I
Sam Rivers | Cyclic Episode
Sam Rivers | Luminous Monolith
The Max Roach Trio | Pay Not Play Not
The Max Roach Trio | Three-Four vs. Six-Eight Four-Four Ways
Sambrasa Trio | Aleluia
Sambrasa Trio | Arrastao
Sambrasa Trio | Clerenice
Sambrasa Trio | Lamento Nortista
Moacir Santos | Coisa N°2
Moacir Santos | Coisa N°3
Moacir Santos | Coisa N°4
The Seeds | Pushin‘ Too Hard
Archie Shepp | Hambone
Wayne Shorter | Deluge
Wayne Shorter | Juju
The Horace Silver Quintet | The Kicker
The Horace Silver Quintet | The Natives Are Restless Tonight
The Horace Silver Quintet | Que Pasa
The Horace Silver Quintet | Song for My Father
Simon & Garfunkel | The Sound of Silence
Nina Simone | Ain‘t No Use
Nina Simone | Be My Husband
Nina Simone | Feeling Good
Nina Simone | I Put a Spell on You
Nina Simone | Nobody Knows You When You‘re Down and Out
Nina Simone | Sinnerman
Nina Simone | Strange Fruit
Nina Simone | Trouble in Mind
Sonny Simmons, Clifford Jordan, Prince Lasha & The Bossa Três | Blue Monk
Sonny Simmons, Clifford Jordan, Prince Lasha & The Bossa Três | Epistle to Train
Frank Sinatra | It Was a Very Good Year
The Sonics | Psycho
The Sonics | Strychnine
The Sonics | The Witch
Sun Ra | Other Worlds
Sun Ra | Outer Nothingness
Sun Ra & His Solar Arkestra | Reflects Motion
Sun Ra & His Solar Arkestra | Space Aura #2
The Supremes | Stop! In the Name of Love
Cecil Taylor Jazz Unit | Nefertiti, the Beautiful One Has Come
Them | Bright Lights, Big City
Them | Here Comes the Night
Stan Tracey | Starless and Bible Black
The Watersons | John Barleycorn
The Who | The Kids Are Alright
Anthony Williams | Memory
Anthony Williams | Tomorrow Afternoon
Anthony Williams | Two Pieces of One: Green
Anthony Williams | Two Pieces of One: Red