An Introduction to R by Venables, W. N., D. M. Smith and the R Core Team. This is the definitive introduction to R. It is included when you install R on your computer (from the R Console menu: Help | Manuals (in PDF) | An introduction to R). If you do not have a background in programming, it may not be the best thing to read at first, but as your understanding increases, this will help to explain the underlying logic of the R system.
R FAQ by Kurt Hornik (Help | FAQ on R). Browse through this and read any sections that look interesting to you. Absolutely read this before you go online to let the world know that you have found a bug in R. FAQ 7.31 is particularly notorious.
R for Mac OS X FAQ by S. M. Iacus, S. Urbanek and R. J. Goedman, and B. Ripley (Help | FAQ on R for Mac OS X) is only downloaded if you are using R on a Mac.
R for Windows FAQ by B. Ripley and D. J. Murdoch (Help | FAQ on R for Windows) is only downloaded if you are using R on Windows.
Free manuals for beginners (just a few, there are many more). These cover the basics and the use of R in statistics.
Using R for Data Analysis and Graphics by Maindonald. A good introduction to using R in 85 pages.
R for Beginners by Paradis. Another good introduction in 72 pages.
The R Guide by Owen. The basics in 53 pages.
A Student's Guide to R by Horton, Pruim, and Kaplan. An introduction to basic statistics using R and R Studio in 114 pages.
icebreakeR by Robinson. The basics plus introductions to the bootstrap, mixed effects modelling, and programming in 155 pages.
Visual Statistics. Use R! by Shipunov. A bit more than the basics in 326 pages plus appendices.
Tutorials
Quick-R by Rob Kabacoff. Provides brief examples using R for specific tasks. Very useful when you know what you want to do, but are not sure how to do it in R.
UCLA Resources for R. Various resources on R including data analysis examples, frequently asked questions, downloadable books and more.
twotorials by Anthony Damico. Two minute video tutorials explaining aspects of R.
R Tutorials by William King. Using R for various statistical analyses.
The R Reference Index (pdf, 3500+ pp) combines the manuals for the packages that are automatically installed with R (Help | Manuals (in PDF) | R reference).
Resources for using Rcmdr - a graphical user interface (GUI) for R. Use install.packages("Rcmdr").
The R Commander: A Basic-Statistics GUI for R by John Fox.
Getting Started With the R Commander by John Fox.
The R Commander: A Basic-Statistics Graphical User Interface to R Journal of Statistical Software 14(9) by John Fox.
R commander: an Introduction by Natasha Karp.
Resources for using R Studio - an integrated development environment (IDE) for R. This is a free stand alone program.
Introduction to RStudio by Oscar Torres-Reyna. A brief introduction to the layout of the RStudio windows.
Using the RStudio IDE. Topics relating to specific features of RStudio.
Introduction to R, RStudio. Basic introduction to R using RStudio.
Useful websites
The R Project for Statistical Computing - the main site.
CRAN Task Views - very useful topical summaries of R packages.
The R Journal - open-access, peer-reviewed journal of the R project for statistical computing
R Help archives via MarkMail. Has someone already answered your question? You can subscribe to the r-help list and ask (and answer questions as your knowledge increases).
Stack Overflow - a web-based forum to ask questions about R.
R Seek Google for R, but usually just using Google and adding R to your query works just fine.
R Bloggers - R news and tutorials contributed by over 750 R bloggers.
 Archaeology and R
MikeMetrics Mike Baxter's page
How to do archaeological science using R by Ben Marwick. An edited volume based on a symposium at the Society of American Archaeology meetings in Vancouver, BC in 2017.
Quantitative Archaeology by Matthew D Harris.