John Wilkes Booth
There is of course no proof of this, but many authors and descendants of Booth have suggested that he did escape, and there have been several attempts by the family to exhume his body to be tested for DNA.
Probably one of the most famous outlaws of the Wild West, Jesse James and his gang robbed a number of banks, stagecoaches, and trains throughout his criminal career, until he was shot in the back of the head in his own house by fellow James Gang member Robert Ford on April 3, 1882 in and attempt to receive the reward on James's head.
Now despite the fact that he was positively identified, there have been rumors going around even from back then that he faked his death, and that he may have lived under an assumed identity even into the 20th century.
The reason behind this is because many people said that he really didn't look like he was suppose to. Of course there is a reason behind this: he had plastic surgery so that he wouldn't look like himself (he even tried to get rid of the famous dimple in his chin). The most likely reason behind this is of course so that he could to live as a free man until he died (which in a ironic way is what happened).
Despite the fact that the remains were found and that dental records confirm that the remains are that of the mad man, there are many people who believe that he did not commit suicide, and that he actually faked his death, and that he may have even lived past 100.
While most people believe that he escaped to either Spain or Argentina, some of the crazier claims are that he either escaped to Antarctica, or to the Moon, or to the inside of the Earth (which some Hollow Earth believers claim), and even another dimension or time period.
While there have been numerous "Elvis sitings" over the years, these could be attributed to Elvis impersonators, or just people who look like him.
The belief that he is alive could simply be the result of fans who loved him so much that they don't want him to be dead.
People who believe this point out that multiple albums with new songs by Shakur have been publish after his death, and while his family says that he recorded the songs before his death, many people still believe this not to be true, and that he is actually continuing to secretly make songs.
Osama Bin Laden
His death is also unique in the fact that no only do some people believe that he is still alive, but that many other people believe he died years before his official death (either as a result of natural causes, or via military actions) and that his body has been kept on ice to be later dumped in the ocean for political proposes.
Notable mention: Paul McCartney
While this is a pretty bizarre conspiracy theory, he isn't the only celebrity that is believed to be really a CIA body double, he just happens to be the most famous case.