Just a few off the top of my head; in no particular order:
Comfortably Numb (especially the first one)
Albatross (and an assortment by Ian Thornley)
Whipping Post (especially Dickey's solo)
I'm So Glad (I believe done on one string; Clapton at his most brilliant and experimental)
I Need Your Love So Bad
Still Got the Blues
Big Love (not really a "solo", but an ultimate solo piece)
Not only does this always give me "the chills" but I'd suspect the following act that day had a few profound moments of introspection standing in the wings....
Not only is it a study in relentless attack, slide mastery and compositional brilliance, but the nonchalance with which Landreth walks on, plugs in and whammmmmm.... he plays like he's double parked on his lunch break!!
Heck, even the wimmens are getting off on it! (1:11)
Keef on Gimme Shelter on the Let it Bleed album. Some stuff from Magic Sam, Otis Rush, Hendrix, Gilmour. Jimmy Page. Pete Anderson and Brent Mason in their prime. Old Muddy Waters where he's playing as close to a "solo" as you'll eve get out of him, Etc. Hank Marvin Apache. Some Jerry Cantrell stuff give me that too but wouldn't be called a "solo".
David Gilmour (PF The Wall) Comfortably Numb, Another Brick In The Wall Pt2
Roland Orzabal (Tears For Fears) Shout
Neil Schon (Journey) Who's Cryin' Now
Alex Lifeson (Rush) La Villa Strangiato
Edge (U2) - The Ground Beneath Her Feet
Jeff Beck - Somewhere Over The Rainbow
Steve Hackett (Genesis) Firth Of Fifth
Mark Knopfler - Brothers In Arms
Lindsay Buckingham (Fleetwood Mac) Go Your Own Way, I'm So Afraid
Terry Clements (Gordon Lightfoot) Wreck Of The Edmund Fitzgerald
Keith Urban - 'Til Summer Comes Around
Yes, I like epic solos that hit safe notes. But let's face it, the reason why all of us play guitar and keep at it for all these years is because we get chills from hearing different guitar parts in the music we hear. I am just trying in my own little way to sink deep enough into the music and play something that would give me chills.