Jimi Hendrix
Eric Clapton
Jeff Beck
Jimmy Page

Didn't see Tom Morello

What, no love for George Harrison and Steve Howe?

Even though off-topic I'm still gonna mention Andres Segovia.

Steve Lukather, Lindsey Buckingham, Eric Johnson, BB King, Neal Schon, Mark Knopfler, Craig Chaquico, Pat Metheney

Jimi Hendrix. End of story.

Odd fact: though I have no connection to the music industry, I've met Eric Clapton twice.

In 1979 he and Muddy Waters hailed the taxi I was driving, off the Edgewater Inn stand, in Seattle. Their scheduled limo had failed to show up and they needed a ride to the airport.

And in 2002 he answered the door at a girl's house I went to visit, I'd prefer not to say where. Told me she'd gone off to attend a sports event.

I guess that if I were the girl, expecting me to show up, but somehow meanwhile I'd bumped into Eric Clapton, and taken him home, I'd have sent him to the front door to offer excuses to me too.

If the pattern holds, when next I meet him, in 2025, I'll remember to get a selfie and an autograph.

And if his guitar is handy, snip a couple of his damn strings

Yea,Tom Morello......a very avant garde guitarist to say the least.
Didn't mean to leave Jerry out earlier. I guess I was thinking living guitarists. But even if the Dead were having a particular off night Jerry could take a solo and put you at ease.....

As an incredible creative pioneer on the electric guitar it would it would most definitely have to be Jimi Hendrix.

Eric Clapton...no less

Eric Clapton is fantastic. Has more of a soft melodic style of playing that's why the ladies love him.

very great in captivating's every woman's heart..
his lyrics..his melodies simply superb!

Pete Townsend, Eric Clapton, Jimi Hendrix

Frank Zappa, I love all those mentioned, but I keep coming back to Frank.

Nina_Nin,
Three of those started out playing in the Yardbirds,and were all blown away when Hendrix arrived in London, If you like Guitarists, have a listen to Zappa, Shut up n play yer Guitar, is a good place to start,
It really is-Virtuosity gone mad, Enjoy:

There are just so many great guitarists and I agree with 99% of the ones mentioned.
Greatest is subjective. Most well-known isn't the same as most talented.

I have seen some extremely talented guitarists that are not top of the charts famous.

Phil Keaggy is a master and loves playing his guitar but many don't know of him because he plays gospel music and uses sampling to create a one-man-band effect.

Phil Keaggy - County Down
http://www.youtube.com/watch?v=qhf0ypN4OuQ

Phil Keaggy - Salvation Army Band
http://www.youtube.com/watch?v=8m2hoNVugKA

Recently I found Bjorn Berge on Youtube. The first video I saw hooked me to his talent.

Bjorn Berge - Mad Fingers Ball
http://www.youtube.com/watch?v=tqcoWFDeb0w

BJORN BERGE "ramblin on my mind"
http://www.youtube.com/watch?v=W3gZ9bIU9FY

Seasick Steve is a very talented hillbilly style that I believe can make music on anything. Playing a one-string homemade guitar and actually making money with it is impressive.

Seasick Steve 1 string diddley bo'
http://www.youtube.com/watch?v=TbefIwp5LoQ

Something a little more conventional...
Seasick Steve - Hobo Low
http://www.youtube.com/watch?v=a33sB3ck28A

Plus there are many many Mexican guitarists that are truly amazing.

Rodrigo y Gabriela- "Hanuman" OFFICIAL
http://www.youtube.com/watch?v=ENBX_v1Po1Y

Mariano Franco - La Malagueña
http://www.youtube.com/watch?v=YZWudNPMJ-g

Uriah Heep - Salisbury
http://www.youtube.com/watch?v=o7Zeo-KfO70

Specifically starting around the 11 minute mark

http://youtu.be/o7Zeo-KfO70?t=687

Just watched Salvation Army Band. Fantastic! Not many sing into their guitar.

Bass strung under left handed
Albert King
Doyle Bramall

Prince. When Clapton was asked "what does it feel like to be the best guitar player of all time?" He replied, "I don't know. You would have to ask Prince...."

'nuff said

Dave Gilmour was doing a live gig soon after the death of Prince,
and during the Guitar Solo of Comfortably Numb, he introduced a section
of the Guitar Solo from Purple Rain, what a complement,
for those interested it's on Youtube

Clapton
BB King ....