As you can tell from the speed and diversity of the responses you have received - this is an extremely popular question. Most people will advise you of their favourite guiatrist, who may not necessarily be the 'greatest'. I will digress from this well-worn path and advise that my favourite guitarist is Jimmy Page, but I think the 'greatest' is Django Reinhardt, from an influential perspective. Enjoy the rest of your responses.
Despite winning all those NME polls in the 80s, I can confirm that Paul Weller is *not* the greatest guitarist of all time. Hard to avoid, in addition to other old favourites being cranked out: Lowell George, Duane Allman, Neil Young, Link Wray, James Burton, Robbie Robertson and, to prove not all great guitarists are white men of a certain age, Elmore James, Richie Havens and Bonnie Raitt.
David Gilmour of Pink Floyd. Not the fastest nor the loudest just the most musical. Sit back and listen to the live version of the closing solo of "Comfortably Numb" and be blown away
For influence: Robert Johnson
For awesomeness: Django Reinhardt
For originality: Jimi Hendrix
For chugging along: George Thorogood
For tophattedness: Slash
For skill and virtuosity all jazz players can wipe the floor with rock players - but so what if they can't rock'n'roll ?
Elmo from Sesame Street...are you being serious, surely it has to be Cliff Richards or the guy who strums really well....em.....Bryan Adams, yeah, Bryan Adams!!!
no one is i suppose, its a matter of opion.but in my opion i'd have to say brian may from queen, that burgandy red guitar that his dad & himself made from an old fire surround i think, and other bits& pieces sways for me excellent.