As guitarists/musicians we have a wide variety of influences, but lets post our absolute favorite guitarists that you don't have to think twice about. Here's mine in order:
1)Alex Lifeson-incredibly tasteful and a true team player. He's always carried himself with class and everytime I listen and/or see him I always make it a point to carry something into my own playing.
2)Tony Iommi-The king/godfather of heavy metal. The amount of killer, classic metal riffs this guy has come up with is staggering. What's even more impressive is that he's done it with different lineups and different eras..."Master of Reality" sounds totally different from "Heaven and Hell."
3)George Lynch-Yeah I know Eddie and Randy are the kings of the '80s L.A. hard rock scene but when I first heard Lynch it was like being hit by a freight train. He had the perfect combination of warm, hotrodded Marshall tone and chops to burn that really struck a chord with me (pun intended!)

I'm a bassist, but I DO have favorite guitarists, although they may not be ones that everyone thinks of immediately:
1) Richard Thompson -- Richard started out with Fairport Convention, struck out with is then-wife, Linda, but has been solo for some time. His influences stretch from Celtic to rock, and he's adept at any style, playing in a flatpick and two-finger style. His solos are melodic and don't always take the usual route. He switches between acoustic and electric with ease. Check out his "Live from Austin, TX" DVD for a great performance with his trio.

2) Tommy Malone of the Subdudes -- Tommy is also the primary singer for the Dudes, who play a mixture of country/rock/New Orleans styles. Tommy plays excellent slide on both acoustic and electric, but I think his guitar work is sometimes overshadowed by his powerful voice. The latest Subdudes CD is the acoustic-based "Flower Petals," but its predecessor, "Street Symphony," gives a truer picture of the band using electric instruments as well. No overdubs on either CD -- what you hear is what they sound like live.

3) Eric Clapton -- My lone "Doh! pick. Of course -- Clapton. From Cream, through Blind Faith, Derek & the Dominoes and his solo career. A great, blues-based guitarist.

Good list, I would say my favorite guitar players start back in the 60's and 70's with:
Ry Cooder-known more for roots rock and slide guitar and of course the sound track to Cross Roads and his collaberation with the Stones and way to many other others to list here.

Manny Charlton of Nazareth-He spanned so many different music genres (Hard Rock,Blues,Metal,New Wave, and Punk)while with Nazareth and his solo efforts, I always admired his diversity.

David Gilmour Pink Floyd for technical guitar playing.

Dave Murray and Adrian Smith Iron Maiden for real finger twisting dual guitar insanity.

I love the soundtrack to Crossroads-especially the dual with Steve Vai.

Awesome pick for Murray and Smith of Iron Maiden. Me and my buddies debate for hours who the better guitar team is-Murray/Smith or Judas Priest's Tipton/Downing.

My favorites... in no particular order

Mark Knopfler
Stevie Ray Vaughan
Joe Walsh
Eddie Van Halen
David Gilmour

Joe Walsh is an interesting choice. Didn't he share guitar duties with the other guys from the Eagles? His solo stuff is kind of hit-or-miss isn't it? His stuff with the James Gang was cool. What is it about his playing that you like?

I think his playing is always memorable, as was Don Felder's. It was never just a lick or a bunch of notes, but a composition... come on... Rocky Mountain Way... it's like a vocal part. Plus his Hotel California solo bits have a little bit of attitude to them, and he's got a great sense of humility and humor. His solo on Dirty Laundry (middle solo, Lukather did the end solo, which is also great) is also really cool. Just my opinion.

Another guy I love is Audley Freed. If you've never heard the first Cry Of Love (band) cd, it's got some AMAZING guitar on it.

I have to tell my Joe Walsh story. Back in 1971, my band was part of a triple bill with the James Gang and Glass Harp (Phil Keaggy). That's a pretty heavy lineup, so naturally our guitarist decided he would blow those two offstage. We did Led Zeppelin's "Heartbreaker," with the big guitar cadenza. right in the middle of it, our guitarist pulled his guitar up passionately and accidentally unplugged himself -- silence. We had no roadies, so he had to sheepishly plug himself back in and finish the solo. This was in a small hall at a college in Ohio, and Joe & Phil were cracking up at the back of the hall.

I saw the Eagles maybe 15 years ago and both Felder & Walsh were great. An amazing band, instrumentally and vocally.

That's a great story and I'll raise you one: I played in a band where the drummer thought he was going to be the next Neil Peart and do an unaccompanied solo during one of our shows. As he's doing these rolls on his snare drum, the snare drum worked itself free from its stand and fell off the drum riser and rolled across the stage. He had to get up from his drum seat, walk across the stage and pick up his snare and set it up again. I don't even know how I finished that gig because I couldn't stop laughing my a## off for the rest of the night.

I also saw the bass player from Argent get trapped under a boom stand when he slid across the stage on hid knees in a "rock moment" and it fell on him. Roadies had to rescue him. So I guess it happens to everyone.

Everyone has a Spinal Tap story.

Jeff Beck - A1 Superbad Mofo. From funk,jazz to metal noise, JB has always caught my ear. His recent foray into the world of electronica suits him as well as any stop off he's made in his career.

Ronnie Montrose - Power Chords as big as your house and a lead tone dripping with presence and multi head delay.

Adam Jones - Great player and uses GK guitar amps.... Like me!

Robin Finck - A great side man for GnR and NIN. Needs to step out on his own. Also needs to not let Trent Reznor cut his hair.

Speaking of Jeff Beck, I have to put in a plug for his current bassist, Tal Wilkenfeld. She's in her mid-20s but looks much younger. What a player! www.talwilkenfeld.com

Not to mention her career when she was just a teenager and turning 20 with none other than Chick Corea. Good luck transcribing that stuff. Even the guys who write bass player magazine have had trouble with it. TOO good.

Don Felder - In my opinion the best lead player I ever heard. Not a fancy shredder. Nothing but Smooth. Tasteful. Class. I saw the eagles a few years ago and Felder was no longer with them. The lead player they had new all the leads verbatim but was lacking some major feel.

Leo Kottke - Fingerstyle twelve string grovin. I have seen him in concert and have never been more impressed. He is a one man show with only a guitar and a mic. There was nothing to hide behind and he didn't need to do any hiding.

John Mayer - I know some of you will poo poo on this but I will say it anyway. I was not a John Mayer fan until I saw him live. He is a tone freak and a very tasteful player. Also a fantastic songwriter.

Lindsey Buckingham - I think Lindsey of Fleetwood Mac is one of the most under-rated guitar players ever. Songs like Never Going Back Again and The Chain are incredible. A very intricate guitar piece and on top of that he sings.

Brad Paisley - Not a huge country fan but wound up seeing him play at a festival in Colorado and was completely blown away. Incredible flat picker.

Andy Mckee- If you haven't heard of Andy, do yourself a favor and look him up on youtube (where he got famous). You will not be disappointed.

I could go on....

I have to bump this one for Andy McKee, and for one of his biggest influences (and I think his teacher for a time) Michael Hedges. I still can't get over his work with Michael Manring (definitely in my top 5 bassists, personally).

And John Mayer is no slouch on guitar either. After seeing him live and not only holding his own with John McLaughlin (Mahavishnu Orchestra composer and solo jazz/fusion MONSTER) but push the guitar player to new extremes, I have nothing but respect for his playing. A fantastic instrumentalist.

I think something needs to be said as well for Adam Jones of TOOL, whose career was made just the way Jimmy Page describes his, "from making mistakes." I think he even sounds a little like Page from time to time with his '76 Les Paul. And he has a way of sounding like nobody else on the guitar. A fantastic player and composer. I also highly recommend checking out his art and the music videos he did for TOOL. A fantastic artist who has really formed his own sound and used it successfully.

Funny story ericseiv, I had once to tape my snare drum on top of my kick pedal case because there were no snare stand in the club I was playing, you can imagine how awful it sounded. I did had a great gig though haha.

Back to the subject:
Jimmy Page, Alex Lifeson and Adam Jones are my favorite guitar players.

After NAMM, I have to add a guitarist to my list. I knew his music before, but something changes when you see an instrumentalist live.

Doyle Dykes gave a master class just before Victor Wooten. He is hands down the best fingerstyle guitarist around. Better than Andy and as much as it pains me to say it, better than Leo. He is a cross between Eric Johnson, Chet Atkins, and Leo Kotkee. What a show. I have some of the audio recorded and if I can figure out how to get it off my iphon, I will post it somewhere.

I'll add that everyone should check out Ben Lacy, who was playing at the Warwick booth at summer NAMM. Tapping & slapping and outstanding solo playing, everything from Beatles to Stevei Wonder to Steely Dan, Michael Jackson and Michael McDonald. Check out his website: www.benlacy.com and also search Youtube for some video.

Yeah, he is awesome Laklander, never seem someone doing that percussive tapping with a electric guitar before.
http://www.youtube.com/watch?v=n6xMf5DwAhA&feature=related
This is a kick ass performance, check it out.