Joe Satriani and Steve Vai come to mind.
Oh…and Ralph Machio. 
I want to second a lot of the ones listed here but I also need to add:
Uli Jon Roth
Lindsey Buckingham
Tuck Andress (I love that man)
B. B. King
Victor Wooten (He plays bass but it is still a guitar)
Bonnie Raitt
Yeah…here is another vote for the Karate Kid. He rocked in that guitar movie with Britney Spears.
I was actually going to mention him, but didn’t. :smack:
Hey, WpgTriniman, I’ll nominate somebody else from your hometown: The late Kurt Winter. He could wring stuff out of that Stratocaster that I’ve never heard anybody do.
Kim Mitchell (ex- of Max Webster)
I can’t believe we got this far withoug anyone mentioning Alex Lifeson (Rush)!
Michel Pagliaro and Billy Workman
Bruce Cockburn
- Jimmy Page - Led Zeppelin
- Tom Morello - Rage Against the Machine
Hmm…can’t think of any more at the moment…
How’s he underrated? It seems like most people who know about him think he’s great.
Hey, this thread is called favorite guitarists, not greatest, so it’s all right if he’s not technically great.
I can’t believe I forgot to mention them! They’re awesome!
I also really like Lou Reed’s playing.
Will Sergeant of Echo and the Bunnymen is also really cool. He does some great riffs.
Eric Clapton
Billy Corgan
Carlos Santana
Slash
For all-out skill, imagination, and consistency I think I like David Gilmour most.
If I could have the talent and ability of one guy it’d be Eric Clapton.
The guys I hear pull off little phrases that make my spine tingle the most frequently, I’d say Jimi Hendrix, Frank Zappa, and Steve Howe (from Yes).
That said, there are tons of guitarists that blow my mind all the time.
Jerry Byrd
Probably the best known steel guitar player, has passes away April 11, 2005 
As usual in these music threads, I end up agreeing with Nitroglycerine
Small Clanger… Kimberly Rew, hell yeah. Guitarist for The Soft Boys (let’s not mention Katrina and the Waves though). He’d be on my list.
Also I’d want to add…
Link Wray
Captain Sensible (The Damned)
Marc Ribot (Tom Waits)
Jo Callis (The Rezillos)
Bob Stinson (The Replacements)
Kirk Kirkwood (The Meat Puppets)
Dallas Good (The Sadies)
Glad to see an old friend, **Jimmy Herring[/m] mentioned. This is guy is really amazing and under-appreciated. Absolutely phenomenal player.
Also glad to see the late, great Michael Hedges mentioned. Although he was so much more than just a guitarist. He damn near -reinvented the damn thing.
Others that I really enjoy are (in no particular order):
Steve Morse
Scott Henderson
Frank Gambale
Lindsey Buckingham
Steve Lukather
Larry Carlton
Jimmy Page
takes a bow for my crappy coding :smack:
Leo Kottke
Chris Smither
The Reverend Horton Heat
Ted Leo
Billy Corgan
Slash
Dave Gilmour
Bassists who deserve mention:
Les Claypool
Stanley Clarke
I’ve never really got big into ‘guitar gods’ like Clapton or even really Hendrix. Their style is not mine, I’m afeared.
Hold on! You guys reminded me of Michael Hedge’s, whose arrangement of Sofa #2 is still the song I am most proud of learning to play.
Joni Mitchell (I can’t believe I’m the first one to mention her).
Nick Drake
Johnny Marr
Emily Saliers (from the Indigo Girls)
Greg Brown (for the way he writes simply but it really supports the music)
Bill Frisell - Noodling jazz occasionally verging into country. He makes you really conscious of the spaces between the notes. Try starting off with the album Good Dog, Happy Man.
Bo Diddley - I saw him a couple times in the past few years and he was simply amazing.
Helios Creed - The music is like a ice pick hammering through your skull. In a good way.
Wow, 77 posts and no one has yet mentioned Andy Latimer of Camel. Sad. One of the great progressive guitarists. He’s not flashy, but he gets a lot of emotion out of his instrument. Go here and listen to the song called “Ice”. It starts out simple, but let it play all the way through and hear what he does after the synth solo. Then try “Chord Change”.
Since this is favorites, and not “best,” I’m going to go with Happy Rhodes. While not a virtuoso on the guitar in any sense of the word (simplistic, compared to the gods already mentioned), I think she’s a master at using her guitar to create atmospheres around her vocals. Most of her recorded songs are keyboard-oriented, which make the guitar songs more special to me. That’s also why I love seeing her live, because she has to play the guitar more.
These songs will illustrate perfectly what I mean (I have her permission to share songs)
Summer (acoustic version)
Prey of the Strange (her very first recording)
Temporary and Eternal (acoustic version)
Ode (another very early song)
A few years ago, right before a concert, she badly cut a tendon and damaged the nerve in her fret hand, a nightmare for a guitarist, and later had to have surgery to repair the hand. Amazingly enough, she went on and performed after going to the hospital. Fans feared she’d never play guitar again, but she can now. She’ll never be the same though. (her story of the accident). She had no medical insurance, so fans got together and sent her donations. She put together a “thank you” CD for fans. It was called the “Left Hand Demos.” 
While I’m here, I’ll add Kevin Bartlett and Bon Lozaga of Project Lo and Gongzilla to my list.
And Steve Hackett, of course.
Oh so many great ones named so far. I can’t really go back and comment on them all, so I will just add a name no one could have possibly put into nomination yet:
Warner Hodges
Don’t know who that is, huh?
'course you could just put on “Last Time Around” and listen.
or “Absolutely Sweet Marie”. But you won’t will ya?