Jimi Hendrix
Jimi Hendrix played guitar upside down and backwards, and to his devout fans' parents, it probably sounded like it. The six-string revolutionary favored a right-handed Fender Stratocaster, slung upside-down across his shoulders, that didn't even need to be restrung: Hendrix taught himself how to hit the strings in reverse order, producing a unique sound and allowing him to alternate between left- and right-handed playing if he so desired. (He could play right-handed but generally preferred not to).
Hendrix learned to play in Nashville blues clubs before touring as a back-up musician for the Isley Brothers and Little Richard. He broke out on his own in 1966, but his career was cut short by a drug overdose in August 1970. Hendrix's use of distortion and wah-wah effects warped and extended notes in ways no other player could quite achieve; for years, right-handed guitarists have tried to emulate his sound, going so far as to put left-handed necks on their own guitars.
There was one technique not impacted by Hendrix's lefthandedness: setting his guitar on fire. For that, he used both hands.