"The earliest documented performance with an electrically amplified guitar was in 1932," according to Wikipedia. The electric guitar was used by Hawaiian Style musicians. George Barnes reportedly recorded the first 2 songs with the electric guitar in 1938.
Now, Rock 'N' Roll without the electric guitar, is a folk song; slap a banjo on your knee and rock with a toothless hockey player on the harmonica. Howstuffworks calls it the best thing since the incandescent light bulb.
In It Might Get Loud -- a documentary on the electric guitar from the point of view of three rock legends, Jack White, the lead vocalist for The White Stripes; The Edge, guitarist for the Irish rock band U2; Jimmy Page, co-founder of the English rock band Led Zeppelin; give accounts of their lives mastering the electric guitar.
Jack White makes a one-string electric guitar from a board, a pick-up and Coke bottle in the film. Jimmy Page wrote a new song for the documentary. And the Edge is featured arranging his song "Get on Your Boots."