This question is basically from Ravi Vakil's web page, but modified for Math Overflow.
How do I write mathematics well? Learning by example is more helpful than being told what to do, so let's try to name as many examples of "great writing" as possible. Asking for "the best article you've read" isn't reasonable or helpful. Instead, ask yourself the question "what is a great article?", and implicitly, "what makes it great?"
If you think of a piece of mathematical writing you think is "great", check if it's already on the list. If it is, vote it up. If not, add it, with an explanation of why you think it's great. This question is "Community Wiki", which means that the question (and all answers) generate no reputation for the person who posted it. It also means that once you have 100 reputation, you can edit the posts (e.g. add a blurb that doesn't fit in a comment about why a piece of writing is great). Remember that each answer should be about a single piece of "great writing", and please restrict yourself to posting one answer per day.
I refuse to give criteria for greatness; that's your job. But please don't propose writing that has a major flaw unless it is outweighed by some other truly outstanding qualities. In particular, "great writing" is not the same as "proof of a great theorem". You are not allowed to recommend anything by yourself, because you're such a great writer that it just wouldn't be fair.
Not acceptable reasons:
- This paper is really very good.
- This book is the only book covering this material in a reasonable way.
- This is the best article on this subject.
Acceptable reasons:
- This paper changed my life.
- This book inspired me to become a topologist. (Ideally in this case it should be a book in topology, not in real analysis…)
- Anyone in my field who hasn't read this paper has led an impoverished existence.
- I wish someone had told me about this paper when I was younger.
Best Answer
Anything by John Milnor fits the bill. In particular, "Topology from the differential viewpoint" made me feel that I understand what differential topology is about, and the "h-cobordism theorem" made me feel that it's beautiful. Many other books and papers by him are wonderful; the first that come to mind are "Characteristic Classes", "Morse Theory", lots of things in Volume 3 of his collected papers.