If I recall from my readings on geisha, the origins are in Noh drama. Kimono worn right over left were reserved for the dead. Ghosts, spirits and such characters who were dead wore them that way, and that is how they're worn on a body during burial rites.

Edited to add: Read from the following books: http://www.amazon.ca/Geisha-A-Life-Mineko-Iwasaki/dp/0743444299

http://www.amazon.ca/Kimono-Paul-Van-Riel/dp/907482241X

According to author Liza Dalby (in her book "Kimono: Fashioning Culture"):

The code specified that all robes should be crossed left side over right in Chinese fashion. Such "sidedness" of clothing is important in many cultures. Precisely because of the natural arbitrariness of left and right, sides can be used to express cultural differences of great import. A garment's sidedness is not something to be reversed lightly. The Chinese considered right-over-left a mark of barbarism. This explains the Japanese decision to abandon their traditional mode. All Japanese robes, including kimono, have wrapped left over right since the Yoro Clothing Code demanded it.

Collars that are worn right-over-left is how the dead are dressed in Japan, so if you're alive and being dressed in kimono, definitely wear the collar left-over-right (an easy way to remember it is "leftover rice", which sounds a lot like "left over right"!).