As a counterpoint to the Strunk and White recommendation, please take a look at this: 50 Years of Stupid Grammar Advice[1]. (Note that it doesn't primarily object to the stylistic advice in S&W, which it calls "vapid" but "mostly harmless". The real objections are to the grammatical claims and advice.)

Two books on writing I strongly recommend:

Clear and Simple as the Truth: Writing Classic Prose[2], exerpt here[3].

Style: Towards Clarity and Grace - this one has gone through countless versions as the publisher seems to re-release it every academic year. (Make used copies obsolete and raise the price.) I prefer the older, shorter versions to the more recent ones. It was clearer itself when briefer! Anyhow, here's an author search on Amazon - look for older used copies[4]. Edit: Just found this outline of the 6th ed. of the book. A good way to see what he covers in a hurry.[5]

The first is not a standard writing guide; it's a thoughtful analysis of what makes a certain kind of writing clear and persuasive. The second is a more nuts-and-bolts guide to writing. They're both excellent.

[1]: http://chronicle.com/article/50-Years-of-Stupid-Grammar/2549...

[2]: http://classicprose.com/

[3]: http://classicprose.com/csx.html

[4]: http://www.amazon.com/Joseph-M.-Williams/e/B001H6MZ40/ref=nt...

[5]: http://www.oxfordtutorials.com/StyleTenLessons.htm