"On Writing Well" is a classic book on writing nonfiction that recently celebrated its 30th anniversary. As my main area of writing is scientific writing, I read it with the intent to learn for my scientific papers.
With this background, my judgement on the book is mixed. There are several chapters that are useful for scientific papers but a good share of the book is written for journalists. The view, which is the view Zinsser himself probably has, is that of a generalist writer who has to explain something to the public. This does often not fit very well with the intention of most scientific papers.
Most useful for me was Part I "Principles" and Part II "Methods". What he explains there is almost universal. He talks about simplicity and style, about words and their correct usage. I especially enjoyed Chapter 10 "Bits & Pieces" in which Zinsser collected short but helpful hints for your everyday writing.
Part III "Forms" includes chapters such as "Writing About People: The Interview" or "Writing About Yourself: The Memoir" that didn't help for my usual tasks. Even Chapter 15 "Science and Technology" was not what I was looking for because it covered much more the journalists's view. To some degree Chapter 16 "Business Writing: Writing in Your Job" could give some insights for my writing.
Overall the book is fun to read and Zinsser proves in it that he is the right guy to listen to on writing well.