As I understand it, when the Russians arrived, the remaining Nazi officials left in the Führerbunker claimed that both Hitler and Eva Braun killed themselves, and were then cremated outside.
I've also heard that the Russians took "Hitler's skull" which, a few years ago, was actually proven not to be Hitler's through DNA evidence.
As a follow up question, I'd like to ask that, IF there was no other physical evidence of his suicide, why would the witness testimony of some of his most loyal friends and officers be considered reliable? Wouldn't it have been just as likely that Hitler fled, and his associates burned another body and lied in order to protect him from pursuit?
Apart from a piece of the top of his skull they also took part of his jaw. The jaw piece is what proved Hitler had died. The Soviets got ahold of Hitler's dental records and were able to match the teeth perfectly. The piece of skull might not be Hitler's (though that claim is still debatable), but the jaw certainly is.