Trying to stick to influential as opposed to those I like the best.
Jimi Hendrix - Show me a guitarist who hasn't tried to play like Jimi.
Les Paul - He is credited with so many firsts and innovations, both for the guitar itself as well as playing it that he has to be on this list.
Eddie Van Halen - Sure, there is Vai, Satriani and others who all have very similar sounds but all of them came after Eddie. He's the one who influenced these guys who came after him and who then took it to the next level. I actually prefer Vai over Van Halen. I agree with the comments about his first album Flex-able which could almost pass for a Zappa album. But Eddie did it first. That's influence.
Jimmy Page - I'll actually say that I don't think he is one of the greatest of all time, but his timing and the massive popularity of the band helped him to influence tons of young guitar players. I'm not a guitarist. I'm a drummer. But my teenage band played tons of Zeppelin. That's influence.
I didn't put Zappa on the list even though I would put him on a list of the greatest guitarists of all time. I think his weirdness factor kept a lot of people from listening to his music. For me growing up Zappa was extremely prominent in my listening activities. So much so that one day when I was 16 or 17, maybe 18, my mother was trying to get into my head and she asked me this question: "Do you think you'll still be listening to Frank Zappa when you're 40 years old?" My immediate answer was "absolutely". And wouldn't you know it, when I turned 40 I had to call my Mom and say to her, "Guess what Mom? I'm still listening to Frank Zappa." And with each milestone birthday I remind her that I'm still listening. My list is short because I'm not up on Robert Johnson or Chuck Berry. I know who they are but not being a guitarist I'm not certain of their influence on players. Now, if this was a listing of influential drummers, I'd be all over that one.
