Overview: The conspiracy argument suggests that Adolf Hitler did not commit suicide on 30th April 1945 as the official story goes, but in fact escaped to South America after faking his own suicide. The story of suicide was fabricated, it is said, to show the leader ended his life heroically.
Official story: Adolf Hitler committed suicide by gunshot on 30 April 1945 in his Führerbunker in Berlin. His wife Eva (née Braun), committed suicide with him by ingesting cyanide. That afternoon, in accordance with Hitler's prior instructions, their remains were carried up the stairs through the bunker's emergency exit, doused in petrol and set alight in the Reich Chancellery garden outside the bunker. The Soviet archives record that their burnt remains were recovered and interred in successive locations until 1970 when they were again exhumed, cremated and the ashes scattered.
--- Note that the whole suicide story rests solely on the testimony of four fanatical Nazis.
The 'evidence' of conspiracy includes:
There never was an identifiable corpse of Adolf Hitler, nor of Eva Braun.
An image of Hitler's skull was presented by Russian officials as proof of Hitler's death (the guardian) however this skull was from a woman under 40, and not of a 56 year old man that Hitler would have been on his death.
Hitler Death Picture: This is the only picture we have been able to find on the internet showing an apparently dead Hitler. It is not verified.
The Gestapo chief, Heinrich Mueller, told his US CIC interrogators in 1948, that he arranged Hitler's escape from Berlin and that Hitler, together with Eva Braun, flew to Barcelona, Spain, on April 26th 1945.
1945: Joseph Stalin told many Allied Leaders that Hitler escaped from Berlin.
1952, Eisenhower is said to have declared: We have been unable to unearth one bit of tangible evidence of Hitler's death. (Source Amazon blurb for Grey Wolf: The Escape of Adolf Hitler by Simon Dunstan and Gerrard Williams)
Grey Wolf: The Escape of Adolf by Gerrard Williams and Simon Dunstan, says Hitler and Braun fled to Argentina, had two daughters. He died in 1962 at the age of 73.
This is the last confirmed picture of Hitler:
Picture of a room in Hitler's bunker
Interesting fact from @UberFacts: Bin Laden's death was announced on May 1st 2011. Hitler's death was announced on May 1st, 1945.