Many people, mostly on the left but some on the wacky side of the right, could not accept the results of a thorough and massive investigation by the Warren Commission, which concluded that Oswald did it alone. Benny Huang sheds some light on why the conspiracy advocates believe what they do. In his article The JFK Assassination As A Window Into The Leftist Mind, he writes:
Huang's analysis is spot on. However, reading through the comments to the article, it is obvious that there are many on the Wacky Right (think Alex Jones) that believe in the conspiracy too, but with a variety of named culprits: LBJ, George Bush the elder, the bankers, etc etc. Read it all at the link above.
With thanks to No Pasaran! for first bringing this article to light.