Hitler was not a normal surname in Germany/Austria/Switzerland. The surname "Hitler" was a variant of the surname "Hiedler" and was used for the first time by Adolf Hitler's father Alois.

Alois Hitler was born Alois Schickelgruber in 1837 to a single mother, inheriting her name. He only took the name "Hitler" when his married uncle, Johann Nepumuk Hiedler (his mother had married Johann Georg Hiedler, his potential father in 1842) left him part of his estate and mandated in his testament that he change his name to "Hiedler" in order to inherit. So, in 1877 Alois Schickelgruber changed his name to Alois Hitler. Whether the difference in writing was a clerical error or intentional is unknown but we known that from this change on, Alois Hitler called himself exactly that in all official documentation and that he is pretty much the only person known to use this surname from the historical records.

As for post-war usage, Adolf Hitler had six siblings and the lineage of one of them, Alois Hitler Jr., still exists to this day. His sons William Patrick Hitler (who served in the Marines during WWII fighting the Axis) and his brother Heinz Hitler were Alois children. Of those, only William Patrick had children, some of whom are still alive today but all changed their names in order to distance themselves from their relative.

Slight variations of the surname exist to this day (Hittler e.g.) and according to the phone book, one other family in Germany has the surname Hitler but in general (probably descendants of one of the other siblings of Adolf Hitler) this name was exclusive to Hitler's family.

Sources:

Ian Kershaw: Hitler.