John Wilkes Booth
Everyone knows that John Wilkes Booth assassinated President Lincoln, and that twelve days later on April 26, 1865 he himself was shot and killed by Union soldiers after he refused to leave the barn that he was in that the soldiers had set ablaze, but there are rumors that Booth was not killed that day, and that in fact a look alike had been shot and killed, and that Booth had actually lived even into the early 20th century.
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.
Jesse James
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.
John Dillinger
On July 22, 1934 notorious American criminal John Dillinger was shot to death by FBI agents in an alley way in Chicago, but ever since then there have been rumors that he really wasn't shot to death, and that who really was killed was just someone who just looked like him (perhaps even a payed body double).
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).
Adolf Hitler
Without a doubt the most evil person in history, on April 30, 1945 Adolf Hitler and his wife Eva Braun killed themselves in an underground bunker in Berlin, Germany. There bodies were removed by Nazi Party loyalist and set on fire so that the Soviet Army couldn't use them as propaganda pieces.
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.
Elvis Presley
Probably one of the most widely believed to be still alive dead people, Elvis Presley died on August 16, 1977, but many still believe that he isn't actually dead (despite the fact that he was in very poor health and abused prescription drugs) and while various reasons have been given for why he is hiding, the most common is that he is actually hiding from the mafia.
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.
Tupac Shakur
On September 7, 1996 rapper Tupac Shakur was shot multiple times in Las Vegas while he was sitting in a car with Suge Knight. Six days later, he died, but some people believe that he did not die, and that he actually survived the attack, and that he has been in hiding every since.
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
On May 2, 2011 in his secret mansion compound in Pakistan, Osama Bin Laden was shot and killed by members of SEAL team 6, and despite the fact that this was even confirmed by Al-Qaeda, because his death photos have not been released, and the fact that he was buried at sea, and the fact that many people unfortunately still believe that he was a government agent, many people believe that his death was faked for political proposes (of course the people who believe that he was a government agent also believe that the government caused the 9/11 attacks...)
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
Paul McCartney gets a notable mention here not because he's dead and that many people think he's alive, but because he is alive and that many people think he is really dead, and that he actually did die in a 1966 car crash (which he had originally been reported to have died in) and that he was replaced by a CIA body double that would keep an eye on John Lennon (who was critical of the war in Vietnam and had political philosophical beliefs that many in the government object to).
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.