| There is a longer (and less often heard) version of this proverb: "Curiosity killed the cat, but satisfaction brought him back." I prefer this one, but it is a later add-on to the phrase.
Most sources I can find say it was originally "care kills a cat," and was first used in the 16th century. "Care" meant "worry" in this case -- too much anxiety is bad for you. The "curiosity" version is first recorded in 1909, probably as a result of the changes in the most common meanings of "care."
Sources:
http://www.writersblock.ca/fall98/a-letter.htm
http://www.xmission.com/~emailbox/phrases.htm
http://www.penmarric.ns.ca/cattails/prose.htm | 
