My teaching situation is a bit different from the others who have responded so far. I do teach an occasional class at the university, but my main job is with a group of hospitals and doctors doing their statistics. As part of that I teach some classes within the hospital system to doctors/nurses/whoever. These tend to be very different students from the undergrads at the university (anyone else ever had a student use the excuse "I was performing surgery" for missing class?).
These classes are less focused on how to do the stats (they will have me do them for them), but more on the concepts so that they can understand the literature that they read, work with me better in designing studies, and do better at writing/presenting the results.
The university where I teach occasionally uses some web based stats program for the intro class (even simpler than minitab in what it can do). I keep trying to talk them into using R (through the Excel interface or RCmdr), but so far have made little progress.
In both situations I am not teaching the students how to use R, but I still use it to demonstrate various concepts. I mostly use simple examples (plots, quick numbers) or those from the TeachingDemos package (that is what it was written for (disclosure of possible conflict of interest in promoting the package: I believe that the package author/maintainer raids my fridge more often than he should)). Even though the students are not learning R itself, they appreciate the concepts illustrated. The mainly GUI based illustrations could be written in any language (but using R means that I can customize them and more advanced students can look at the code themselves and learn more).
The R-based code usually does not phase the students even though they have not leaned R themselves yet. Those that do not understand it just look at the results, but many do understand the main ideas. For example, at the university, the standard course materials use the 1970 draft lottery as an example for showing scatterplots, correlation, relationships and other concepts. As a bit of a teaser there is a slide that asks if the relationship could be due to chance (this is before we get into the inference part of the course). We don't come back and answer that teaser until the last week of class (when we have done hypothesis testing an regression). But I like to show the students a simple simulation at the time of the teaser with simple code such as:
out <- replicate(10000, cor( sample(1:366), 1:366 ) )
hist(out)
sum( abs(out) > 0.18 )
quantile( out, c(0.025, 0.975) )
2.5% 97.5%
-0.1021715 0.1003527
It takes less than a minute to explain that 1:366 is the numbers from 1 to 366 and that the sample function randomizes the order. The replicate function and the rest of the code is fairly self explanatory even for people who don't know any programming, but this example clearly shows that the amount of correlation in the 1970 draft lottery was unlikely due to random chance as well as what values we would expect to see by chance. Some of the students will stay after class and ask about R, I explain that it is not part of the official class, but that if they are interested here is the website and additional info ...
So, I think that R is a great tool for teaching statistical concepts even when R is not the statistical package being used for the course itself.