The Leslie rotary speaker cabinet was widely used in the 60's, and its characteristic sound was popularised by such acts as Procol Harum on "A Whiter Shade of Pale", Jimi Hendrix on "Little Wing" and others...
While normally used with an organ, because it is a separate unit, any musical source, such as an electric guitar, as heard in Cream's "Badge" or Pink Floyd's (who have also used the Leslie speaker on a piano in "Echoes" and on backing vocals in "Time") "Any Colour You Like", can be played back through a Leslie speaker, creating a wide range of surprising and dramatic effects.
John Lennon's voice was processed through a Leslie speaker for the highly experimental song "Tomorrow Never Knows" on The Beatles' 1966 album Revolver. Ozzy Osbourne sings through a Leslie speaker on the song "Planet Caravan" on Black Sabbath's 1970 breakthrough album Paranoid. Jerry Garcia's voice was processed through a Leslie Speaker on the song "Rosemary" from the Grateful Dead album Aoxomoxoa.

A Leslie speaker yesteryear (left) and a Tube Rotosphere today
Pete "Overend" Watts of the band Mott the Hoople linked his bass through a Leslie on the track "Alice" from the album "The Hoople". Tori Amos also makes much use of a Leslie speaker on Boys For Pele, a highly experimental album with piano, harpsichord, harmonium, and clavichord. On such songs as "Horses", the Leslie effect is made obvious as it is switched on and off for different parts of the song, itself a continuous piano piece, allowing for a strong comparison in the piano's sound. Ron Bushy, drummer for the 60's acid rock group Iron Butterfly, utilized a Leslie Speaker during the drum solo of the 17-minute epic In-A-Gadda-Da-Vida, giving the solo a distinct phasing effect.
Of course, now the Leslie Cabinet is a rare, very expensive collectors item, but since the late 60's several FX pedals have been made that try to capture that unique Leslie sound - chorus and phaser pedals were directly inspired by the Leslie.
The best thing is - now you can find those pedals in all price ranges: from the perfect Leslie sounds of the Hughes & Kettner Tube Rotosphere (used by Noel Gallagher of Oasis) to cheaper Behringer Vintage Phaser, which still delivers some very good Leslie sounds.
Give it a try - plug your guitar, microphone, keyboards or even bass to one of those pedals and let your creativity flow - like it did so many years ago, when artists first discovered the Leslie!
Some pedals we recommend, if you want to capture the Leslie sound:
Hughes & Kettner Tube Rotosphere Mk II (by far, the best attempt yet to capture the Leslie sound)
Behringer VINTAGE PHASER VP1
Electro Harmonix Small Stone US Version
Electro Harmonix NANO CLONE CHORUS PEDAL
Dunlop UNI-VIBE