Paco De Lucia
Leo Kottke
Nick Drake
Kaki King
Kevin Shields
Joey Santiago
Johnny Marr
Jimmy Page
Jimi Hendrix
Roy Buchanon . . .I saw him about 6 months before he died at a little bar in Pittsburgh called Graffiti. Real nice, intimate set. He never really recorded a whole lot that captured his talent. . .my favorite song by him(on vinyl) was “Can I change my mind” with Billy Price vocals. It seemed as though he never let a song stand in the way of a solo, but this one was all about the song, and his understatement here made it great.
Adrian Below - Saw him at the same venue. Totally unlike what I was expecting. Not a lot of guitar effects or animal noises, just rock. Did “Pretty Woman” as a tribute to Roy Orbison, as he had died the previous day. He did noodle around with his (I’m pretty sure it was) stereo guitar effects, which were apprently new to him. It was cool to see him just play around with them for ten minutes or so.
So many great guitarists. . .Stevie Ray Vaughan(who I saw do a 5 minute solo behind his back. . .), Robert Randolph(not mentioned thus far), Eddie Van Halen, Carlos Santana, Steve Vai. . .Eric Johnson does some great work, of course David Gilmour(haunting, screaming solos), Keith Richards, and I’m not going to ‘sort of’ mention Lindsey Buckingham. I full-heartedly endorse him as a great guitarist. Ever see “The Dance?” he could’ve sleep-walked his way through this ‘best of’ live concert full of songs he’s known for 20 years, but he brought something new to every song, and just blew me away.
George Harrison, Jimmy Page, Brian May. . .wow, it’s astonishing the brilliance we’re subjected to on a daily basis and how we grow to take it for granted.
These are good days.
-DocJon
Danny Gatton. Saw him in Arlington, VA and will never forget it.
Bob Mould … back before he decided he wanted to fiddle around with turntables and samplers and sequencers and machines that go blip and bloop.
How about Charo?
I’ll mention a couple of guitarists from my hometown:
Randy Bachman
Lenny Breau
[QUOTE=DarkSideoftheFloyd]
David Gilmour.
Upon preview, I see someone had already put him down.
…The child is grown, the dream is gone…
[QUOTE]
With a sig line, appropriately enough, from the album with so many world class guitar soloes they had to stuff two in that song 
His other stuff is really great too (esp. Obscured by Clouds, and TFC) but The Wall is by far and away the best guitar recorded in the history of mankind.
Hell-fucking-yeah to both of those. Amen!
Mine:
Kevin Shields (My Bloody Valentine) - Wrote the book on “guitar as instrument of sound design.” Makes similar contenders (the Edge, Adrian Belew) sound like dead-fucking amateurs by comparison. Probably the most underrated guitarist of all time, especially since big-dick Guitar Mags pretend he never existed.
I think I’m the first to mention these, which is surprising, but what about Thurston Moore and Lee Ranaldo (Sonic Youth)?
Also, Rhys Chatham. You’ve not heard the guitar until you’ve heard “An angel moves too fast to see,” which features 100 guitars and a rhythm section.
Segovia, Leo Kottke and Chet Atkins are the only guitarists I can reliably identify just by hearing the music.
If I was going to pick my starting five for the “basketball team of guitarists” it would have to be these:
Center: Eric Clapton
Power Forward: Jimmy Page
Small Forward: Stevie Ray Vaughn
Shooting Gaurd: Dav Navarro
Point Gaurd: Hendrix
Sorry
Dav --> Dave
Sorry Dav -->Dave
Why did you assign a particular guitarist to a particular position?
I agree with many who have been listed, so let me add:
David Bromberg
Ian Anderson (Tull’s flute player, who also does a great deal of the accoustic work on their albums.)
Snooooopy:
I don’t know, its just my personality; I like basketball.
Clapton- Best all-around guitarist in my opinion therefore I’d want him centering my team.
Page: IMHO, my favorite guitarist, he has to be the #2 option.
Vaughn: Just a slight shade below Page therefore small forward.
Navarro: A really creative guitarist. kind of like the ‘Steve Kerr’ of guitars.
Hendrix: He runs everything. You can’t go wrong with his leadership. Like the Michael Jordan/Dave Stockton/Jason Kidd of guitarists.
Sorry John Stockton. I’m a mess.
Thus far and Yngwie Malmsteen but no Ritchie Blackmore? Hang your heads! {I’m pretty sure he hasn’t been mentioned}: check out his solo on the live version of Child In Time, off Made In Japan. Widdly-wee show-off heaven.
Since the op question is Who are your favorite guitarists … personal taste rather than an attempt at objective judgement, these are the ones I find myself listening to most rather than the “best”, which would be another list (almost) entirely.
In no order:
**Kimberly Rew ** - c’mon, anyone else even know who he is?
Ricky Wilson - early B52’s did he ever learn to tune a guitar “properly”?
Anyone playing a **Steely Dan ** guitar solo (this would be a long list)
**David Gilmour ** - I lean towards the Animals stuff, just a sucker for harmonies I guess.
Pete Townshend - The Who’s rhythm guitarist, he’s really quite good.
**Jimmy Page ** - another decent rhythm player, can produce decent solos on occasion.
**Frank Zappa ** - one word WatermelonInEasterHay known to play stupid/fast stuff too.
And to show I’m not totally rockist – the guys with 12 incredibly agile fingers:
Michael Hedges
Leo Kottke
Billy Diffy, ex of The Cult (currently playing with Jerry Cantrell as Cardboard Vampyres). Words cannot describe his crunching riffs and sweet, bluesey solos.
Jeff Martin from Canadian band The Tea Party. I’ve recommended them around here before, and I cannot speak highly enough of them. Their earlier works are deep rooted in Eastern influence, and their later stuff is a lot more to the rock side but still maintains the Eastern melodies. They kind of have that flavour of Led Zeppelin’s ‘Kashmir’ mixed with pounding rhythm and excellent rock riffs. Just…wow!
I forgot a few:
Ottmar Liebert
Nick Webb and Greg Carmichael of Acoustic Alchemy
Carlos Montoya
Chet Atkins