Rand Wilcox collected and introduced a lot of robust methods for estimating and testing. These robust methods do not rely on the typical parametric assumptions and therefore are robust against violations of these assumptions.

Wilcox provides R functions for every method described in his book "Introduction to Robust Estimation and Hypothesis Testing" (Amazon Link). This is a great thing, as many authors publish amazing new methods, but give no hint how to actually use them. With Wilcox' functions, every applied researcher with some knowledge of R can employ robust statistics.

Here's a review of the book:

This text focuses on applied aspects of major modern and robust statistical methods. Early chapters explain the aims and mathematical foundations of modern methods. The heart of the book describes methods for addressing common problems in ANOVA and regression, with a minimum of technical details, and judges their merits using multiple criteria, giving advice on which ones to use for various situations. Chapter exercises are included. The book assumes a previous introductory statistics course and background on basics of ANOVA, hypothesis testing, and regression. For this third edition, S-PLUS functions are no longer supported. Instead, R functions are supplied.
Reference and Research Book News, Inc.


Together with Rand Wilcox I provide an R package for these functions, the WRS package (Wilcox' Robust Statistics).

Installation of the WRS package


WRS cannot be hosted on CRAN, as CRAN demands help files for every user-visible function. This has not been done for WRS (yet). For the time being, a somewhat more complicated installation routine has to be used.
For installation, please follow the instructions given here.

Blog post about WRS and it's functions





References:
Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing, 3rd Ed. Academic Press.
Wilcox, R. (2012). Modern Statistics for the Social and Behavioral Sciences: A Practical Introduction. CRC Press.
Wilcox, R. R. (2010). Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy. Springer, 2nd Ed.
Wilcox, R. R. (2009). Basics Statistics: Understanding Conventional Methods and Modern Insights. New York: Oxford.
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