This one is going to take some time. For one thing, I like a lot of music. For another, for the sake of this list, I am going to start with one song per artist, adding to the individual lists once I've gotten everyone in once. (Some will also have more selections listed in my "Favorite Singers" posts.)
At the moment I can't narrow the Beatles to one song, so no selection yet. And, as you can see, I am going through stuff somewhat alphabetically — although with a side trip into my MP3 — so don't think I've missed artists yet. As with the other lists, some of the things here are just for grins, but they still got the grin.

2Gether, "The Hardest Part of Breaking Up."
ABC, "When Smokey Sings."
Cannonball Adderley, "Mercy Mercy Mercy."
Alien Fashion Show, "Detroit Swing City."
Mose Allison, "Your Mind Is on Vacation."
Allman Brothers Band, "Jessica."
Louis Armstrong/Oscar Peterson, "That Old Feeling."
Art of Noise/Tom Jones, "Kiss."
Ashford & Simpson, "Solid."
Marcia Ball/Lou Ann Barton/Angela Strehli, "Fool in Love."
B-52s, "Private Idaho."
The Band, "The Night They Drove Old Dixie Down."
Gato Barbieri, "Last Tango in Paris."
Beach Boys, "God Only Knows."
Belmonts, "My Sweet Lord."
Chuck Berry, "Too Much Monkey Business."
Beta Band, "Dry the Rain."
Elvin Bishop, "Travelin' Shoes."
Blackout All Stars, "I Like It."
Blind Boys of Alabama, "Rain."
Gary US Bonds, "Out of Work."
Booker T & The MGs, "Hip-Hug-Her."
James Brown, "Cold Sweat."
Tim Buckley, "Once I Was."
Jimmy Buffett, "Cheeseburger in Paradise."
Cactus, "You Can't Judge a Book by Its Cover."
James Carr, "Dark End of the Street."
Joe "King" Carrasco and the Crowns, "Buena."
Cars, "Just What I Needed."
Chambers Brothers, "I Can't Stand It."
Chic, "Good Times."
Chicago, "I'm a Man."
Eric Clapton, "Let It Rain."
Kelly Clarkson, "The Trouble With Love Is."
Clash, "I Fought the Law."
Patsy Cline, "She's Got You."
Joe Cocker, "You Can Leave Your Hat On."
Leonard Cohen, "In My Secret Life."
Nat King Cole, "A Blossom Fell."
Mitty Collier, "I Had a Talk With My Man Last Night."
Marc Cohn, "Walking in Memphis."
Elvis Costello, "Allison."
Robert Cray, "Right Next Door."
Cream, "White Room."
Dandy Warhols, "We Used To Be Friends."
Miles Davis, "It Never Entered My Mind."
Derek & The Dominos, "Tell the Truth."
Desmond Dekker & The Aces, "Israelites."
Detroit, "Rock and Roll."
Dixie Chicks, "Goodbye Earl."
Dominos with Clyde McPhatter, "Harbor Lights."
Ian Dury & The Blockheads, "Hit Me With Your Rhythm Stick."
Dyke & The Blazers, "Funky Broadway."
Bob Dylan, "Like a Rolling Stone."
Emotions, "Best of My Love."
Fania All-Stars, "Ella Fue."
Fear of Strangers (AKA The Units), "Hat and Coat."
Roberta Flack, "Ballad of the Sad Young Men."
Four Tops, "Reach Out I'll Be There."
Erma Franklin, "Piece of My Heart."
Georgia Satellites, "Keep Your Hands to Yourself."
Gnarls Barkley, "Crazy."
Al Green, "For the Good Times."
Lenis Guess, "Workin' for My Baby."
Roy Hamilton, "Don't Let Go."
Isaac Hayes, "By the Time I Get to Phoenix" (full-length version).
Don Ho, "Shock the Monkey."
Whitney Houston, "Exhale (Shoop Shoop)."
Howlin' Wolf, "Spoonful."
Jackson 5, "Forever Came Today."
Elton John, "Levon."
Albert King, "Born Under a Bad Sign."
B.B. King, "To Know You Is To Love You."
Kinks, "Money Talks."
John Lennon, "Beautiful Boy."
Julie London, "Cry Me a River."
Nick Lowe, "Marie Provost."
Les McCann/Eddie Harris, "Compared to What."
Paul McCartney, "Maybe I'm Amazed."
Delbert McClinton, "B Movie."
Madness, "One Step Beyond."
Manhattans, "Kiss and Say Goodbye."
Bob Marley, "No Woman No Cry."
John Mayall, "California."
Buddy Miles, "Them Changes."
Miracles, "Way Over There."
Van Morrison, "Tupelo Honey."
Jason Mraz, "Curbside Prophet."
Tracy Nelson, "Down So Low."
Joan Osborne, "One of Us."
Randy Newman, "Political Science."
Graham Parker, "You Hit the Spot."
Freda Payne, "Band of Gold."
Teddy Pendergrass, "Choose Me."
Persuasions, "Buffalo Soldier."
Madeleine Peyroux, "Dance Me to the End of Love."
Wilson Pickett, "Man and a Half."
Pretenders, "My City Was Gone" (version at the Rock Hall opening concert).
Prince, "Erotic City."
John Prince, "Spanish Pipedream."
Ramones, "Rock and Roll High School."
Otis Redding, "Cigarettes and Coffee."
Smokey Robinson, "Cruisin'."
Vicki Sue Robinson, "Turn the Beat Around."
Rolling Stones, "Gimme Shelter."
Sam & Dave, "Soothe Me."
Son Seals, "I Believe to My Soul."
Patti Smith, "Because the Night."
Spinners, "Rubberband Man."
Dusty Springfield, "Breakfast in Bed."
Bruce Springsteen, "Atlantic City."
Edwin Starr, "25 Miles."
Barrett Strong, "Money."
Supremes, "Some Things You Never Get Used To."
Billy Swan, "I Can Help."
Rachel Sweet, "Baby Let's Play House."
Talking Heads, "Psycho Killer."
Johnny Taylor, "Your Love Is Rated X."
Temptations, "Just My Imagination."
Irma Thomas, "Wish Someone Would Care."
Toots & The Maytals, "Pressure Drop."
Traveling Wilburys, "End of the Line."
U2, "I Still Haven't Found What I'm Looking For."
Luther Vandross, "If Only for One Night/Creeping."
Velvet Underground, "Sweet Jane."
Waitresses, "Christmas Wrapping."
Wallflowers, "One Headlight."
War, "The World Is a Ghetto."
Dionne Warwick, "Walk On By."
Was (Not Was), "Walk the Dinosaur."
Muddy Waters, "Let's Spend the Night Together."
Katie Webster, "Who's Making Love."
Mary Wells, "Two Lovers."
Who, "Baba O'Riley."
Lucinda Williams, "Hot Blood."
Jackie Wilson, "Doggin' Around."
Womack & Womack, "APB."
Stevie Wonder, "I Believe When I Fall in Love It Will Be Forever."
Wynonna, "Just Like New."
Neil Young, "Down by the River."
Timi Yuro, "Hurt."
Warren Zevon, "Play It All Night Long."
ZZ Top, "Sharp Dressed Man."