Some of the names that leap readily to mind:
Bob Dylan
Billy Corgan
Kurt Cobain
Scott Stapp
Jim Morrison
I’ll probably think of more later…
Dave Matthews
Missy Elliot
Good Egg - you do mean besides Brittney Spears, don’t you? (Why does anyone refer to her as a “singer” anyway).
Britney Spears sings crap songs but her voice is OK. I agree with Bob Dylan - he doesn’t have the world’s best singing voice.
And as bad as his voice is, his harmonica playing is even worse.
Tiny Tim Besides having the worst voice, he was the ugliest famous singer also.
Baby Jesus cried when he sang.
I haven’t heard her sing, but there’s indirect evidence for Jean Seberg. I mean, how bad do you have to be when you’re in a musical with Clint Eastwood and Lee Marvin and yours is the only voice that gets dubbed?
Another vote for Dylan.
Jim Carroll (his voice sours milk that’s still in the glands)
It’s probably just me, but James Brown (love his music, love his dancing, his voice drives me nuts)
Yoko Ono
He’s dead now, but Anthony “what kind of fool YAAAAAAAAAAAAAM Iiiiiiiiiiiiiiiiiiiiiiii” Newley
[Lee Marvin voice]IIIII… waaass… boorrrrn… underrrr…a wandrrrrrrr’nnn starrrrr[/Lee Marvin voice]
I have to disagree on Kurt Cobain. I think he had a wonderfully melodic and haunting voice.
I’ve always though that Vince Neil sucks pretty hard.
Ashlee Simpson was exposed on SNL but maybe those lip-synching pop tarts go without saying?
The obvious answer, Lou Reed.
And a close followup for Gordon Gano of the Violent Femmes.
Neal Young
Tom Petty
The 1985 Chicago Bears
Biz Markee
Yoko Ono is my too-obvious choice. As for people who allegedly possess musical talent:
Alanis Morissette
Kris Kristofferson - fine songwriter, but really tuneless voice
Jennifer Lopez - only can pass as a singer with a whole range of studio tricks - does she even perform “live”?
Paula Abdul - another singer with a thin, studio enhanced voice, and she judges “talent,” what a joke.
There are many others that are way overrated.
Nobody’s said CELINE DION yet.
We 'ave a winnah.
Ridiculous. You may hate Celine Dion - I sure do - but it’s preposterous to say she can’t sing. She can certainly carry a tune and has great control and projection.
Paula Abdul, I thought, was a pretty logial choice; she never really could sing, and what you hear in her songs was very heavily fixed up electronically to sound good. Jennifer Lopez is the same thing. Avril Lavigne is an infamously inept singer live whose voice sounds mysteriously fixed up in recordings. Bob Dylan, say no more.
A choice I’d throw out that hadn’t been picked yet is ghe guy who heads up Green Day. Jesus.
My vote goes to Eddie Vedder…his voice bugs me in itself, but he’s also guilty of establishing a style of singing that every male rock star and his brother has emulated since roughly 1992…
Bob Dylan
Neil Young
Johnny Cash
The Spice Girls
Mick Jagger
Lou Reed
Iggy Pop
With the obvious exception of the Spice Girls, you’ve just listed all of my heroes…are you trying to hurt me? 
Englebert Humperdinck always struck me as a pretty crappy singer.