Lots of great lists (nice one @audi-owe!), many of my faves---but not all---already mentioned.
Al Anderson (The Wildweeds, solo, NRBQ)
Dave Edmunds (Love Sculpture, solo, Rockpile)
Albert Lee (Heads Hands & Feet, Emmylou, The Everly Brothers, solo)
Ry Cooder
James Burton (Ricky Nelson, Elvis, Emmylou)
George Harrison
Steve Cropper (Booker T & The MG's)
Paul Burlinson (The Johnny Burnette Rock 'n' Roll Trio), a fave of Jeff Beck.
Don Rich (Buck Owens Buckaroos)
Roy Nichols (Merle Haggard)
Richard Thompson
Kenny Vaughan (Lucinda Williams, The Fabulous Superlatives, solo)
Nokie Edwards (The Ventures)
Scotty Moore (Elvis)
Carl Perkins
JJ Cale
Buddy Miller
Danny Gatton
Evan Johns
Tony Rice
Albert King
Freddie King
There is a separate category reserved for three whose influence exceeds all others:
Grady Martin
Hank Garland
Merle Travis
I am tempted to bring up the subject of the large number of UK guitarists included in lists not containing the original guitarists the UK guitarists are emulating. But I won't ;-) .