Peter Frampton.
Like a great wine, Peter Frampton has just gotten better with age. He was my favorite guitarist as a kid and he remains my favorite guitarist today. Frampton proves that making great rock and roll isn’t about speed. It’s about feel and conveying a message. I had never seen the following video until today, and the solo at 3:46 literally made me weep. Among dredging up fond memories from 1976, Lines On My Face is my absolute favorite Frampton tune. Yeah, he’s best known for being the first to really rock the talk box, but Lines On My Face always showed to me the depth of his passion, and even 40 years later, his playing still moves me.
Guitar Gear 
Dawg, how can you have just one? I like, in no particular order, all of the following guitarists a LOT:
Billy Gibbons
Jimmy Page
Jeff Beck
Hendrix
Jake E. Lee
C.C. DeVille
Eduardo Van Halenioni
and about 500 others,.I should also put Frampton on the list.
Like you, I have a list of my favorite guitarists, among them are:
Satch Slash Michael Hedges Les Paul
…and many, many others. But topping my list is Peter Frampton. There’s something in his playing and performance that has always moved me like no other guitarist.
I would add all those guys, too, except I’m not very familiar with Michael Hedges. And I’ll also agree that Frampton does put something incredibly special into his work–this recent release of “Lines on My Face” is a great example; it’s almost better than the original–but I could never choose just one. If I did, it would be a shootout between Billy Gibbons (for awesome tone), Jake E. Lee (for speed and tone), and Jimmy Page (for all around tone and innovation). Fortunately, though, I can dig ’em all and I do! Gotta hand it to Frampton for making that long lost axe sing like it’s really happy to see him again! That was an awesome solo.
Like I said, I literally wept when I heard that solo; so unlike the original, but unmistakably Peter Frampton.
Yeah, it’s like he never went away. Sounds just like himself with all the passion and phrasing, but somehow more mature.