Charlie Christian:

Charles Henry "Charlie" Christian (July 29, 1916 – March 2, 1942) was an American swing and jazz guitarist.

Christian was an important early performer on the electric guitar and a key figure in the development of bebop and cool jazz. He gained national exposure as a member of the Benny Goodman Sextet and Orchestra from August 1939 to June 1941. His single-string technique, combined with amplification, helped bring the guitar out of the rhythm section and into the forefront as a solo instrument.

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Wes Montgomery:

Considered by many to be the greatest jazz guitarist of all time

"Wes Montgomery was certainly one of the most influential and most musical guitarists to ever pick up the instrument... He took the use of octaves and chord melodies to a greater level than any other guitarist, before or since... Montgomery is undoubtedly one of the most important voices in Jazz guitar that has ever lived—or most likely ever will live. A discussion of Jazz guitar is simply not thorough if it does not touch upon Wes Montgomery"

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Slash:

The guitar genius who was a member of Guns 'n Roses and Velvet Revolver, et al... He paved the way for hard rock black guitarists like Tom Morello of Rage Against the Machine.

"Slash has received critical acclaim as a guitarist. In 2005, he was named "Best Guitarist" by Esquire, which congratulated him on "beating the comeback odds with a surprisingly legitimate and vital outfit, Velvet Revolver."Slash was awarded the title of "Riff Lord" during Metal Hammer's fourth annual Golden Gods awards in 2007.In 2008, he was ranked No. 21 on Gigwise's list of "The 50 Greatest Guitarists Ever,"and in 2009, he was named runner-up on "The 10 Best Electric Guitar Players" list in Time, which praised him as "a remarkably precise player."In 2011, Rolling Stone placed Slash at No. 65 on their list of "The 100 Greatest Guitarists of All Time."

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BB King:

If you think of "the blues," BB and Lucille is the first thing that comes to mind. The Godfather of the Blues, not much can be said about this man that hasn't already been said. Clean, technical picking with so much soul made BB a household name all over the world.

"King was born on a cotton plantation in Berclair, Mississippi, and later worked at a cotton gin in Indianola, Mississippi. He was attracted to music and the guitar in church, and began his performance career in juke joints and local radio. He later lived in Memphis, Tennessee, and Chicago, and toured the world extensively. King died at the age of 89 in Las Vegas, Nevada, on May 14, 2015, from congestive heart failure and diabetic complications."

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Eddie Hazel:

Not too many of you may know this name, but any guitarist can tell you he was the baddest funk guitarist who's ever lived. Parliament, Funkadelic, and the whole funk movement benefitted from this groundbreaking guitarist. He's the reason why I started to play as a kid.

"Born in Brooklyn, New York in 1950, Hazel grew up in Plainfield, New Jersey because his mother, Grace Cook, wanted her son to grow up in an environment without the pressures of drugs and crime that she felt pervaded New York City. Hazel occupied himself from a young age by playing a guitar, given to him as a Christmas present by his older brother. "

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Prince:

IMHO the most talented pop musician of all time. Prince could sing, play guitar, drums, keyboard, and trumpet. He was a brilliant songwriter and an even better performer. And standing at only 5'3'', he was also a damn good basketball player.

"Prince Rogers Nelson was an American singer-songwriter, multi-instrumentalist, and record producer. He was a musical innovator who was known for his eclectic work, flamboyant stage presence, extravagant dress and makeup, and wide vocal range. His music integrates a wide variety of styles, including funk, rock, R&B, new wave, soul, psychedelia, and pop. He has sold over 100 million records worldwide, making him one of the best-selling artists of all time"

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Jimi Hendrix:

Plain and simple, the greatest guitarist who ever lived. Yep, that's pretty much all I got.

"Born in Seattle, Washington, Hendrix began playing guitar at the age of 15. In 1961, he enlisted in the U.S. Army and trained as a paratrooper in the 101st Airborne Division; he was granted an honorable discharge the following year. Soon afterward, he moved to Clarksville, Tennessee, and began playing gigs on the Chitlin' Circuit, earning a place in the Isley Brothers' backing band and later with Little Richard, with whom he continued to work through mid-1965....

Although his mainstream career spanned only four years, he is widely regarded as one of the most influential electric guitarists in the history of popular music, and one of the most celebrated musicians of the 20th century. The Rock and Roll Hall of Fame describes him as "arguably the greatest instrumentalist in the history of rock music"

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The Above are the ones who influenced my playing the most, below are others who are all supremely talented, but for the sake of brevity did not do a bio.

ETA... Several more guitarists have been recommended thanks to some knowledgeable posters. I've added some of them below in addition to a sample of their musical genius. Thanks to all contributors!

Buddy Guy
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McKinley Morganfield (Muddy Waters)
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Robert Johnson
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George Benson
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Albert King
In studio w/ Stevie Ray Vaughn... y'all have to watch this!
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Curtis Mayfield
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Tom Morello
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Chuck Berry
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Kevin Eubanks
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Stanley Jordan
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Hiram Bullock
playing with all time great and icon Les Paul:
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Vernon Reid
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Freddie King
Pure Soul!
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Sam John Lightnin' Hopkins
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Howlin' Wolf(Chester Arthur Bennett)
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This post was edited on 2/6/17 at 12:42 am