What is R?
If you are evaluating whether you should learn and use R, these videos explain what R does and why it is worth learning. David Smith from REvolutions provides an Introduction to R.
 Dice News presents a two minute quick overview of R
 Courtney Brown presents a 7 minute video on why he encourages his students to learn R.
 J.D. Long presents an hour long video conference on how he came to use R.
Introductory R
If you have just started learning R, these videos show you how to do basic data analytic tasks in R. Rvideos provides around 20 videos providing an introduction to R on topics such as bootstrapping, ANOVA, Graphs, Dates, Sampling, Help, and more.
 ramstatdavid has around 25 videos on YouTube each of around 5 minutes. Many of the videos are on producing plots in R.
 LearnViaWeb has around 15 introductory R videos. Topics include loops, time series, installing R, reading and writing data, writing a function, GLM, and using random numbers.
 Decision Science News has two ten minute video tutorials providing an introduction to R.
 wildscop on YouTube has eight introductory tutorials on R. Topics include installing R, using help, opening files, interacting with the console, manipulating matrices, and plotting.
 ahmetrics on YouTube has five tutorials on R on topics such as trellis plots, reading Excel data, simple linear regression
 Learning R Toolkit has a six module course on R with videos. The first two modules are free.
 regionomics on YouTube has around 5 videos on R interspersed with videos on other topics. Topics include an introduction to R, Rcmdr, and Discrete Choice models.
 Dr. Thomas MacFarland has a series of introductory lectures on R using the Tegrity viewer. It assumes very little prior knowledge of computing or statistics. When I tried it, Tegrity worked better in Firefox than in Chrome.
 off2themovies2 on YouTube has around 20 introductory tutorials on R
 mattstat on YouTube has 7 introductory tutorials on R
 MrIanfellows on YouTube has 3 videos providing examples of using the Deducer GUI to interact with R.
Intermediate and Advanced Materials on R
If you know the basics of R and are interested in learning about a particular topic related to R, the following videos are great. I find it useful to hear how experts talk about R in order to get a sense of how to speak and think about R. Drew Conway makes available a set of videos through VCASMO. The talks are drawn from a range of presenters. The list is growing and at the time of posting includes talks on: ggplot2, Social Network Analysis in R, SQL and R, Python and R, optimisation and R, Zelig, and more.

Hadley Wichkam has a four part video short course on graphics with R.
It is particularly good if you want to learn
ggplot2
 David Mease provides a complete video course on Data Mining using R and Excel
 McStatsTutorials on YouTube has 6 videos on Time Series. A couple of videos demonstrate how to perform analyses using R.
 For my own videos, see the Video Tag of my blog. For example, a 34 minute video analysing Winter Olympic Medal data using StatET and R..
Related Resources
If you enjoy learning about data analysis through videos, you may also want to have a look at my earlier post on fulllength mathematics and statistics video courses. These are great if you need to consolidate more fundamental mathematical and statistical concepts. I also have a post with links on Getting Started with R.If there are links to videos on R that I have left off the list, feel free to post a link in the comments.