To avoid bombarding this thread with a gigantic sterile list of random musicians, I'll say Fred Frith because he was fantastic in Henry Cow and did great solo work of varying styles, especially "Guitar Solos"; Derek Bailey because he was one of the most significant free improvisers ever; and Sonny Sharrock because nobody else did guitar as well in free jazz / avant-garde jazz. Somebody might bring up James Blood Ulmer on that note but I could never get into him much.
John McLaughlin, Duane Denison, Kevin Shields, Buzz Osbourne, J. Mascis, Robert Fripp, Grant Green, Frank Zappa, Trey Spruance, Jimi Hendrix, Andy Gill, Dave Navarro, Devin Townsend, Snakefinger, Elliott Smith, Vernon Reid, Adrian Belew, Josh Homme, Tony Iommi, Eddie Hazel, John Frusciante, Keith Levene, Mark Knopfler, Stuart Braithwaite, Kim Thayil, James Blood Ulmer, Steve Vai, Nick Drake, Andy Partridge, Billy Zoom, Johnny Marr, East Bay Ray, Wata, Greg Ginn, Joe Satriani, D. Boon, Ron Asheton, Dr. Know, Graham Coxon, , Steve Albini, Yamamoto Seiichi, Doug Martsch, T. Rex, Michael Karoli, Zoot Horn Rollo, Ian Mackaye, Tom Verlaine, Glenn Branca, Tim Sult, Eric Clapton, Django Reinhardt, Trey Anastasio, Larry LaLonde, and Sterling Morrison
Oh my goodness, respect for listing Zoot Horn Rollo and Tom Verlaine. And that reminds me I oughtta listen to that Residents album with Snakefinger on it. I heard a tiny bit of You yes yes yes or whatever the track is called and I knew I'd have to eventually.
The latter one, that's the one I was thinking of, but I didn't know he was on more than that at all. I did also hear Eskimo. Don't distinctly remember any guitar parts unless he played other instruments.
The best guitarist is Tosin Abasi (along with a very legitimate case being made for Zappa as well), my favorite though would have to be either Akerfeldt, Hendrix, Roger Waters, or Devin Townsend though.
I'm not going to list the common answers (Hendrix, Slash, Cobain, etc) because I probably don't listen to their music and... they're obvious.
Joe Cocchi and Jay Van Schelt (Within the Ruins): [link] Just listen to that whole song. (There are no lyrics so don't just dismiss it in case you dislike metal vocals) The rest of that album contains great guitarwork, but this song takes the cake.
Per Nilsson and Jonas Kjellgren (Scar Symmetry): [link] I've always loved Scar Symmetry's guitar sound and work. It works perfectly with the band's overall "theme". (I just wish their old vocalist, Christian, had remained--the new vocals are great, but c'mon, we all know Christian is secretly the Norse god of vocals)
Tosin Abasi and Misha Mansoor - Progressive metal guitarists (or should I say Djent) Luca Turilli - Neoclassical Guitarist Dimebag Darrell - Thrash/Groove metal? Robert Fripp - You ought to know him if you've heard of King Crimson. Django Reinhard - Gypsy jazz shredder! XD
Frank Zappa: [link] David Gilmour: [link] Steve Hackett: [link] (that sound you hear at around 2:30 is tapping in 1973) All three of Iron Maiden's guitarists: [link] Brian May: [link] Luca Turilli and Alex Starapoli: [link]