What is the single most influential book every statistician should read? If you could go back in time and tell yourself to read a specific book at the beginning of your career as a statistician, which book would it be?
 A: I say the visual display of quantitative information by Tufte, and Freakonomics for something fun.
A: Andrew Gelman's interesting book recommendations are here:
http://thebrowser.com/interviews/andrew-gelman-on-statistics
A: In addition to "The History of Statistics" suggested by Graham, another Stigler book worth reading is
Statistics on the Table: The History of Statistical Concepts and Methods
A: On the math/foundations side: Harald Cramér's Mathematical Methods of Statistics. 
A: For a clear exposition of what should be in social science journal articles (assistance if you're writing or peer reviewing) I like The Reviewer's Guide to Quantitative Methods in the Social Sciences. In particular I like the table desideratra as a synopsis of the minimum that a paper (article, thesis, dissertation) should contain. The chapters are separated by analysis technique, which is nice. I think the book has wider applications than "just" the social sciences as the techniques covered are used across many fields.
Quite early on, so perhaps not covered by the question, I was introduced to Ott's Introduction to Statistical Methods and Data Analysis. It's quite expensive, but is a wonderful resource at showing the underlying statistical models for various GLM methods. I dream of the day that journals require articles to contain show the formula of the statistical model tested.
For checking test assumptions, looking at the effects of various options within a test, and so forth, this is the one book I wish I had when I was studying. I have the previous edition and it is one of the best general resources I have purchased because of the clear and consistent manner in which information about the tests is laid out. It contains nice examples illustrating the test(s), and does not require the reader to have a particular statistical package in order to follow the expositions.
A: Here are two to put on the list:
Tufte. The visual display of quantitative information
Tukey. Exploratory data analysis
A: Fooled By Randomness by Taleb
Taleb is a professor at Columbia and an options trader. He made about $800 million dollars in 2008 betting against the market. He also wrote Black Swan. He discusses the absurdity of using the normal distribution to model markets, and philosophizes on our ability to use induction. 
A: *

*Michael Oakes' Statistical Inference:  A Commentary for the Social and Behavioral Sciences.

*Elazar Pedhazur's Multiple Regression in Behavioral Research.  If you can stand the immense detail and the self-important tone.

In case you're interested, I've reviewed both on Amazon and at https://yellowbrickstats.com/favorites.htm
A: I have read the above recommendations and was surprised to find that most of the people who answered the question were people who are not statisticians themselves. With 2 or 3 exceptions ... 
As an industrial statistician who also happened to work with social scientists and health professionals I would say that if I could take only one book with me to a desert island it would be George E.P Box, Statistics for Experimenters (Wiley). In his inimitable humorous and lucid style he explains the essence and the philosophy of building mathematical models for real data. Rigorous thinking, no mathematical frivolities, no nonsense, teaches us to think statistically, plot and visualize whatever you can. A masterpiece of a competent applied scientist (chemical engineer turned statistician). Always fun to read again.
A: The Elements of Statistical Learning from Hastie, Tibshirani and Friedman http://www-stat.stanford.edu/~tibs/ElemStatLearn/ should be in any statistician's library ! 
A: Rice: Mathematical Statistics and Data Analysis
A: Lots of good books already suggested. But here is another: Gerd Gigerenzer's "Reckoning With Risk" because understanding how statistics affect decisions is more important than getting all the theory right. In fact number one sin of statisticians is failing to communicate clearly. His book talks about the consequences of poor communication and how to avoid it.
A: I am no statistician, and I haven't read that much on the topic, but perhaps 
Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
should be mentioned? It is no textbook, but still worth reading.
A: Probability Theory: The Logic of Science
A: Darrell Huff -- How to Lie with Statistics
A: I am going to go ahead and propose a standard textbook in the field. I am talking about Probability and Statistics by DeGroot and Schervish, first published in 1975.
This book has served as a textbook for many students and is considered a classic, rightfully so in my opinion. It covers topics such as combinatorics, distributions, Bayesian statistics, likelihood inference and regression analysis. As far as I know no other textbook is so thorough so I believe it is a must-have.
A: I learned a great deal from the Bible of Bayesian statistics:
Jose Bernardo and Adrian Smith (2000) Bayesian Theory.
A: It would probably be Bayesian Data Analysis by Gelman or Deep Learning with Python. But that's a bit like taking streptomycin to the middle ages. These were not written when I started my career and quite a few things from the books would have been big news back then. Some of the most influential things everyone should know are in no single source though (perhaps they should be, but...).
A: Not a book, but I recently discovered an article by Jacob Cohen in American Psychologist entitled "Things I have learned (so far)."  It's available as a pdf here.  
A: Long ago, Jack Kiefer's little monograph "Introduction to Statistical Inference" peeled away the mystery of a great deal of classical statistics and helped me get started with the rest of the literature.  I still refer to it and warmly recommend it to strong students in second-year stats courses.
A: I wouldn't argue that either of these should be considered "the most influential book... [for] statistician[s]", but for those who are just starting to learn about the topic, two helpful books are:


*

*Robert Abelson, Statistics as Principled Argument  

*Paul Murrell, Introduction to Data Technologies
A: I think every statistician should read Stigler's The History of Statistics: The Measurement of Uncertainty before 1900
It is beautifully written, thorough and it isn't a historian's perspective but a mathematician's, hence it doesn't avoid the technical details. 
A: William Cleveland's book "The Elements of Graphing Data"  or his book "Visualizing Data"
A: The Essential Guide to Effect Sizes: Statistical Power, Meta-Analysis, and the Interpretation of Research Results by Paul D. Ellis
This book if a "must have" for everyone conducting any scientific research, especially one that comes not from pure stats/maths. The book below extends the first one regarding confidence intervals.
Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta-Analysis by Geoff Cumming
A: "Most influential" is a very different notion from "everyone should read". I am not qualified to answer the first - you'd need someone who is an historian of statistics - but for the second, here are some:

*

*Statistics as Principled Argument by Robert Abelson should be read by anyone doing or using statistics in the pursuit of science, humanities, etc.


*William S. Cleveland's two books on graphics: The elements of graphing data and Visualizing Data.  For statisticians, I'd put these ahead of even Tufte's work, not because Tufte isn't worthwhile but because a) Cleveland wrote with statisticians as his intended audience and b) Cleveland based his recommendations on experimental data about how people look at graphs, rather than intuition.


*Exploratory Data Analysis by John Tukey.  It's dated but valuable - you can do a lot with a pencil and paper and  a brain (at least, if your brain is as good as Tukey's!)
A: Kennedy's A Guide to Econometrics contains a wealth of practical advice about a wide range of statistical analysis.  It's somehow both incredibly information-dense and easy to read, and I still learn something new every time I pick it up.
Wooldridge's Introductory Econometrics has a good amount of this kind of discussion too, but as an introductory textbook it is more self-contained.  I wish I'd had a course based around it.
