Communication and computation:
The Sense of Style, Steven Pinker, 2014. This lovely book uses cognitive science to offer practical advice on structuring your sentences, paragraphs and overall narrative.
The science of scientific writing. George Gopen and Judith Swan. American Scientist. 1990. This article has helped generations of scientists express themselves with force and clarity. A brief summary of Gopen's method for revising your work can be found in this blog post.
The Elements of Style, by William Strunk and E.B. White, has been reliable guide to clear, elegant prose for decades. Some of its advice is a bit pedantic by today's standards, but it remains a great resource.
The Visual Display of Quantitative Information, Edward Tufte, 2001. This is the 2nd edition of a classic, but really any of his books will inspire you with creative, engaging graphics, while also reminding you to minimize visual clutter. You can buy his books (and much more) directly from the author. There's also a free Tufte in R package that produces beautiful graphs based on his practices.
The blog Flowing Data, by statistician Nathan Yau, has many beautiful examples of data visualization. He offers a variety of tutorials for R-based graphics for paid subscribers.
Practical Computing for Biologists, by Haddock and Dunn (2010), is a particularly good place to start learning shell scripting, Python and R, the increasingly common tools needed for Big Data Biology.
More topics to come.