And nobody’s picked Gilmore? Shocker
David Gilmour of Pink Floyd fame (David Gilmore is a jazz guitarist) is my favorite guitarist of all time.
He has certainly influenced me to no end. But I honestly don't know if he has had an "influence" on the guitar playing public as much as the others mentioned. I'd like to think so, but some would argue that Gilmour was the net result of influences from so many previous great players, and therefore his influence is not as discrete.
So if I'm going to allow my personal influences to color my judgement, my personal Mount Rushmore is:
David Gilmour
Neil Young
Alex Lifeson
Glenn Tipton/KK Downing
But going back to the original intent of who I think influenced guitarists and guitarism in general (did I just invent a word?) over the generations, letting just a bit of my favoritism into it, maybe this:
Jimi
EVH
Gilmour
Chuck Berry or maybe BB King or maybe Django
Or maybe Jimmy Page - his rock'n'roll persona may have been more of an influence than his technical skill or "feel", I suppose (which some could very well say about Slash). Page was a rock icon to me in high school, but it didn't stick through college when I gravitated heavily to Floyd.
I dunno, I still think this is an impossible task. OTOH, that is also what is so great about guitar playing - there are so many awesome influences to be found throughout the history of the instrument.
For example, I was just listening to some Echo and the Bunnymen last night (long story as to why...) and was impressed at how well that music has withstood the years - more guitar in there than I remember. A major influence? No, not for me, not even a minor influence for my personal experience. But they probably did influence Radiohead and other bands.