Equivalent of a boxplot for normally distributed data? If I plot some data in function of a categorical variable in R, I get the standard boxplot. However, the boxplot displays non-parametric statistics (quantiles) that don't seem appropriate for normally distributed data.
What is the equivalent of the boxplot for normally distributed data (ideally, something based on confidence intervals?) ? How do I get these plots with R?
 A: Plotting categorical vs continuous variables with box-and-whiskers plots is, as far as I know, fairly common and appropriate for normally distributed data. 
That said, you might be interested in adding additional information (although again, what follows applies to non-normally distributed data as well):
Beyond the question of where the compared distribution peak, getting an idea of the dispersion and the skewness of your data is important. Boxplots will give you some insight into that (by comparing interquartile ranges and the symmetry of each boxplot, for instance), but this remains limited.
Using violin plots, for instance, give you a detailed view of the kernel density of your distribution, and thus highlight "better" the underlying distributions compared to boxplots. 
In R, you can use the ggplot2 library, and use a geom_violin() layer.
require(ggplot2)
p <- ggplot(mtcars, aes(factor(cyl), mpg))
p + geom_violin()
p + geom_boxplot(notch=T) # if you want to compare 

You can also overlay your plots with additional information (e.g. position of mean and standard deviation).
To plot the 1st sigma:
up <- function(x){ mean(x,na.rm=T) + sd(x,na.rm=T)}
down <- function(x){ mean(x,na.rm=T) - sd(x,na.rm=T)}

p <- p + geom_violin() +
stat_summary(geom="point", fun.y= up, size=4, colour="gray50", shape=0,data=mtcars) +
stat_summary(geom="point", fun.y= mean, size=4, colour="gray50", shape=16,data=mtcars) +
stat_summary(geom="point", fun.y= down, size=4, colour="gray50", shape=0,data=mtcars)

I hope this helps.
A: First of all I agree with Momo's comments.  Boxplots are appropriate for normally distributed data as well as any other distribution for continuous variables.  There is no relevance to confidence intervals when discussing boxplots for sample data.
However I think there are ways to customize boxplots to normal distributions by adding lines to show 1 sigma and 2 sigma points and compare them the 68th and 95th percentiles that they should match for normally distributed data.
