I divide this into several categories. One category is recordings of songs, second category is performance of songs. Then there are the stages of my life when I first encountered the song in question. Without a doubt, my eclectic musical tastes were formed in the 1960s, growing up in New York, so I've limited my lists to my most impressionable years, and only to recorded versions of songs. If I included live versions of songs, the list would be pretty endless.

As a teenager, there were several artists' influences that really struck a deep chord in me. The biggies were the Beatles, the Doors, and Laura Nyro.

The Beatles songs that most influenced me were:

All My Loving
I Saw Her Standin' There
Can't Buy Me Love
Norwegian Wood
Blackbird
Tell Me Why
You Can't Do That
Baby You Can Drive Ny Car
Get Back
For No One
Within You/Without You
In My Life
Good Day Sunshine
You're Going to Lose That Girl
Let it Be
Fool on the Hill
You've Got to Hide Your Love Away

The Doors:

Crystal Ships
Soul Kitchen
People Are Strange
Break on Through
Riders on the Storm
Light My Fire

Laura Nyro (some might remember some of these as covered by other artists like Blood, Sweat and Tears and Fifth Dimension):

And When I Die
Poverty Train
Save the Country
Up on the Roof
I am the Blues
Eli's Comin'
Sweet Blindness
Gonna Take a Miracle
Wedding Bell Blues

Then as a teen, there was everyone else after the above, but these are songs that all blew me away (and still do when I hear them):

Sounds of Silence (also the album)-Simon and Garfunkel
Fionnghuala-Bothy Band
Good Vibrations-The Beach Boys (also the entire Pet Sounds album)
What's Goin' On-Marvin Gaye
Who Knows Where the Time Goes-Sandy Denny
Lyke Wake Dirge-Pentangle
My Father-Judy Collins
Compared to What-Les McCann and Eddie Harris
Steve's Song-The Blues Project
Bring the Boys Home-Freda Payne

And then the happy hits music of the era, the artists and the songs (can't separate the two) that I think of when I am remembering all that youthful passion:

Young Rascals-Groovin, How Can I Be Sure, Good Lovin', A Beautiful Morning, People Got to Be Free, Groovin, and I Ain't Gonna Eat Out My Heart Anymore

War-All Day Music, Cisco Kid, Slippin' Into Darkness, The World is a Ghetto, Me and Baby Brother

And then, there is the music of my older sibs that I still LOVE when I hear these songs:

Peppermint Twist-Joey Dee and the Starliters
Soldier Boy-The Shirelles
Wake Up Little Susie-Everly Brothers
Cathy's Clown-Everly Brothers
All I Have to do is Dream-Everly Brothers
Tears on My Pillow-Little Anthony and the Imperials
The Loco-Motion-Little Eva
Runaway-Del Shannon
Quarter to Three-Gary and the US Bonds
Twistin' the Night Away-Sam Cooke
Bring it on Back To Me-Sam Cooke