He wrote his own speeches.

There is some difficulty in "proving" this as many collections of Hitler's speeches are often just excerpts of speeches rather than full text, so not all of the styles can be verified to be consistent across the board. I am told he also had a very distinct written style for his speeches with larger characters to accommodate his eyesight.

It was common practice for statesmen to write their own speeches at this point in time. Goebbels also wrote his own.

He wrote all of his own speeches, and even wrote Mein Kampf from his jail cell. In The Life and Death of Adolf Hitler by Robert Payne (if I'm remembering correctly) it says that his very first speech was a flop. He couldn't hold the audience's attention and was heckled. He used that experience to perfect his stage presence, and became one of history's most powerful speakers.

Not exactly a speech, but when Denmark was invaded, a poorly translated flyer was dropped with the heading "OPROP!"

Leonhard Kaupisch, a german General, mentioned to a danish journalist that the text for the "OPROP!" flyer was written by Hitler himself, after not being satisfied by a draft by Kaupisch. Furthermore it was claimed that Hitler translated it to Danish himself.

source: Vilhelm la Cour: Danmark under Besættelsen, Vol. I Page 111,(picture text)

*EDIT * It looks like I was wrong about the translation part! See other post: https://www.reddit.com/r/AskHistorians/comments/31hbvi/did_hitler_have_a_speech_writer_or_speech_writers/cq43c5z

In his memoirs (Inside the Third Reich), Albert Speer, a member of Hitler's inner circle and reputedly his closest friend, strongly implies that Hitler wrote all of his own speeches, and states in unambiguous terms that he wrote all of his "important" speeches. Relevantly, Speer recounts that before the Nuremberg Rally (an annual NSDAP rally held between 1923 and 1938), Hitler would retire to his residence at Obersalzberg for several weeks just to write the several long speeches he would deliver.

It's worth pointing out that Speer only joined Hitler's inner circle sometime after the latter became Chancellor, so he might not be able to account for Hitler's beer hall years. That being said, I would find it bizarre if a politician transitioned from not writing his own speeches out-of-office to writing his own speeches in-office.

(Edits for accuracy, clarity.)

According to Kershaw, Hitler composed his own speeches. Indeed they were the only form of paperwork that he spent any time on - often working for days on end on their preparation. In later life, when ensconced in government, he dictated to secretaries but the content and editing was entirely his own. His earlier beer hall speeches usually comprised little more than a series of rough notes - just a hew headings and key points that he'd touch on during his rambling sermons.

Source: Ian Kershaw, Hitler