Conspiracy theories are generally large, over-reaching conspiracies to try to cover up a secret, or get something done (sinister or not). JFK is the most well-known series of conspiracies, along with 9/11 conspiracies, Illuminati, the Freemasons and other secret societies.

Urban legends are small, and have a much smaller impact. No one knows where they came from, as they generally happen to “a friend of a friend,” or “one time X happened.” They also vary greatly in detail. A popular urban legend in my area is that a homocidal maniac escaped an insane asylum in a bunny suit (it was Halloween, so no one thought anything of a man in a bunny suit). He then axed some people to death, or hung them off of a bridge. A less deadly example would be Bigfoot.

http://en.wikipedia.org/wiki/Urban_legend
http://en.wikipedia.org/wiki/Conspiracy_theory