Inspired by another thread, and not finding this topic with a quickie search…
Of singers who were known for a wide repertoire (i.e., not one-hit wonders), which ones had a definitive signature song?
For example:
Wayne Newton…Danke Shoen
Ray Charles…Georgia on my Mind
Aretha Franklin…Respect
Frank Sinatra…Strangers in the Night (or is it NY, NY?)
Jim Nabors…Impossible Dream
OK, go…
Tony Bennett: “I Left My Heart In San Francisco”
Alice Cooper - Schools Out for Summer
Garth Brooks - I got friends in Low Places
Ethel Merman- I’ve Got Rhythm
Jim Croce - Bad Bad Leroy Brown
Harry Chapin - Cats in the Cradle
Barbra Streisand – People
Tom Jones – It’s Not Unusual
Tom Lehrer – Poisoning the Pigeons in the Park
Bobby Darin - Mack the Knife. He closed his weekly TV show by performing the song.
Dean Martin - Everybody Loves Somebody Sometime. Also, That’s Amore.
Sammy Davis, Jr. - The Candyman.
More likely, Pollution or New Math.
I think far more people were familiar with the songs he performed on That Was The week That Was.
No, Tom Lehrer’s signature song is The Irish Ballad. I’d be lying if I didn’t say that.
Fanny Brice – My Man
Al Jolsen – Swanee
Kate Smith – When the Moon Comes Over the Mountain
Lena Horne – Stormy Weather
Eddie Cantor – *Makin’ Whoopee *
Nat “King” Cole – Unforgettable
Marlene Dietrich – Falling in Love Again
Peggy Lee – *Fever *
Sophie Tucker – *Some of These Days *
Bob Dylan - Blowin’ in the Wind.
Bruce Springsteen - Born to Run.
Billy Joel - Piano Man.
And I’ll add “Friends in Low Places” for Garth Brooks – though I understand real country fans feel that distinction should go to “The Dance”.
Oh no, it’s I Hold Your Hand In Mine.
Al Green - Let’s Stay Together
B.J. Thomas - Raindrops Keep Fallin on my Head
Janis Joplin - Summertime
Doris Day - Que Sera, Sera
I always consider God Bless America to be a signature song of Kate Smith , as well as When the Moon Comes Over the Mountain
Jo Stafford - You Belong To Me
Dinah Shore - Buttons And Bows
Andy Williams - Moon River
Anita Bryant - Paper Roses
Judy Garland - Over The Rainbow
Liza Minnelli - Cabaret
Doris Day - Que Sera, Sera
Or Everything’s Coming Up Roses.
That was Lt. Hurwitz. 
Jerry Lee Lewis – Great Balls of Fire or Whole Lotta Shaking Going On
Johnny Cash – I Walk the Line
Donovan – Sunshine Superman
Elton John – Candle in the Wind
B-52s: Love Shack (although I personally believe it should be Rock Lobster, I bow to The God of Higher Recognition)
Cyndi Lauper: Girls Just Want to Have Fun
Culture Club: Do You Really Want To Hurt Me
The Bangles: Walk Like An Egyptian
Rickie Lee Jones: Chuck E’s In Love
Nirvana: Smells Like Teen Spirit
Guns N’ Roses: Welcome To The Jungle
Billy Idol: Rebel Yell
Carly Simon: You’re So Vain
Otis Redding: (Sittin’ On) The Dock of The Bay
The Carpenters: Close To You
Joan Jett & The Blackhearts: I Love Rock ‘n’ Roll
Procol Harum – A Whiter Shade of Pale
Jethro Tull – Aqualung
Allman Brothers Band – Whipping Post
Jefferson Airplane – Somebody to Love or White Rabbit
They Might Be Giants - Birdhouse in Your Soul (not to put too fine a point on it)
Jonathan Coulton - Code Monkey
Kingston Trio - MTA
Public Enemy - Fight the Power
Lehrer clearly doesn’t have one, though I’d bet the Silent E song would be more widely recognized than any of the ones mentioned so far (just not connected with him).
James Brown - I Got You (I Feel Good)