Was Adolf Hitler half or quarter Jewish?

Answer

Often suggested, sometimes claimed, but no established historian buys into what is probably just an urban legend.
There have been rumours that Hitler was one-quarter Jewish and that his paternal grandmother, Maria Schicklgruber, had become pregnant while working as a servant in a the household of a Graz Jew called Franberger. During the 1920s, the implications of these rumours along with his known family history were politically explosive, especially for the proponent of a racist ideology. Opponents tried to prove that Hitler, the leader of the anti-Semitic Nazi Party, had Jewish or Czech ancestors. Although these rumours were never confirmed, for Hitler they were reason enough to conceal his origins.

 

Answer

No. The Hitler family was Roman Catholic.
Hitler's grandfather was not Jewish. The standard version of the story focuses on Hitler's paternal grandfather. Hitler's father's mother is said to have worked as a maid for a Jew and there were rumours that Hitler's father was actually the employer's biological child. No evidence for this has ever been found.
Although there is no evidence that Hitler had a Jewish grandfather, supposedly his grandmother refused to reveal the identity of her child's father to her death. There was a suspicion that it was her Jewish employer, but there is no evidence of this, and Hitler certainly never spoke of it.
Hitler certainly hated Jews, as one can read in his book, 'Mein Kampf'. Most Austrian children were raised with a fear, mistrust and hatred of Jews, going back to medieval times, supported by the Catholic Church, that Hitler was born into. Hitler was filled with hatred towards many groups and people, and was a very angry man, as is obvious if you listen to his speeches.

To add to the answers
- I understand that Hitler made a point of destroying the building that would have held his father's birth certificate so the proof one way of the other was destroyed. (History Channel Documentary)
(Observations:
a. In the case of any illegitimate child whose mother refuses to name the father one would expect the entry in the Register of Births to be unrevealing and simply state 'Father: unknown'. In other words, it would have been uninformative in this respect.
b. It is true that the building(s) and the churchyard were destroyed in 1938 on Hitler's orders. He was presumably was nervous about some possible 'dark secret'. However, it's anyone's guess what it was. There has, for example, been speculation about a history of incest or insanity in his family. Perhaps, for that matter, the entry had been tampered with, for example, when his father changed his name in 1876 from from Schicklgruber to Hitler. The 'standard' story about a Jew named Frankenberger in Graz as the paternal grandfather has been discredited. However, it has allowed devotees of psychohistory a field day.
c. Presumably the records were open to public inspection between the time when Hitler first hit the headlines and the Anschluss in 1938. In other words, oponents had already had 14-15 years to look for spicy information. - Joncey).
 

Answer

"There are rumors that the 19-year-old Jewish Boy, from the Jewish family Frankenberger, made Hitler's mother Klara Hitler pregnant. There is not enough information to prove whether or not he was really part Jewish, because when Adolf Hitler came to power, he destroyed all the Birth Certificates, Personal/Private Information, etc. of his family.
Therefore, this debate remains a mystery. Many say "No", many say "Yes". But no human being knows for sure... "
(even though 'Jewish' is specifically a religion it also refers to a collective groups of people and a culture). Click on the links below for more info:

 

Answer

Ian Kershaw, "Hitler ...", Vol. 1, pp. 7-9 dismisses the story as nonsense. At the time when Hitler's grandmother worked as a servant in Graz for a family supposedly called Frankenberger (the 1830s) Jews were completely banned from living in Graz (and the whole province of Steiermark - Styria).
What's more, according to Kershaw, study of directories of Graz and the like for the 1830s and 1840s doesn't reveal any family called Frankenberger in Graz at all.
In other words, it's an urban legend.
No, he was a Roman Catholic.