Well, that's the claim in this hilarious bit by Toronto homeless activist Victor Fletcher:
Asked to explain how he found out that Stephen Harper “secretly” shares Adolf Hitler’s birthday, let alone what it might mean, Fletcher says ,“I’m satisfied I didn’t make it up, okay?”Wikipedia seems to think Harper's birthday is April 30th. The neat thing about Wikipedia is you can look up days of the year and find out who has a birthday on them. Harper shares his birthday with Queen Juliana, Willie Nelson, Kristin Dunst, and (the same year) Paul Gross(!).
Hitler's birthday is close: April 20th. (A day he shares with Wop May, Carmen Electra, and Napoleon). Hitler actually does die on Harper's birthday, if that counts for anything. Ribbentrop, the Nazi foreign minister who may have been fooling around with King Edward`s mistress, happens to share a birthday with our Prime Minister. Is that good enough for the conspiracy set?