This example use the default boxplot() function and the irisdata frame.

> head(iris)
  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

Simple boxplot (Sepal.Length)

Create a box-and-whisker graph of a numerical variable

boxplot(iris[,1],xlab="Sepal.Length",ylab="Length(in centemeters)",
           main="Summary Charateristics of Sepal.Length(Iris Data)")

Boxplot of sepal length grouped by species

Create a boxplot of a numerical variable grouped by a categorical variable

boxplot(Sepal.Length~Species,data = iris)

Bring order

To change order of the box in the plot you have to change the order of the categorical variable's levels.
For example if we want to have the order virginica - versicolor - setosa

newSpeciesOrder <- factor(iris$Species, levels=c("virginica","versicolor","setosa"))
boxplot(Sepal.Length~newSpeciesOrder,data = iris)

Change groups names

If you want to specifie a better name to your groups you can use the Names parameter. It take a vector of the size of the levels of categorical variable

boxplot(Sepal.Length~newSpeciesOrder,data = iris,names= c("name1","name2","name3"))

Small improvements

Color

col : add a vector of the size of the levels of categorical variable

boxplot(Sepal.Length~Species,data = iris,col=c("green","yellow","orange"))

Proximity of the box

boxwex: set the margin between boxes.
Left boxplot(Sepal.Length~Species,data = iris,boxwex = 0.1)
Right boxplot(Sepal.Length~Species,data = iris,boxwex = 1)

See the summaries which the boxplots are based plot=FALSE

To see a summary you have to put the paramater plot to FALSE.
Various results are given

> boxplot(Sepal.Length~newSpeciesOrder,data = iris,plot=FALSE)
$stats #summary of the numerical variable for the 3 groups
     [,1] [,2] [,3]
[1,]  5.6  4.9  4.3 # extreme value 
[2,]  6.2  5.6  4.8 # first quartile limit
[3,]  6.5  5.9  5.0 # median limit
[4,]  6.9  6.3  5.2 # third quartile limit
[5,]  7.9  7.0  5.8 # extreme value

$n #number of observations in each groups
[1] 50 50 50

$conf #extreme value of the notchs
         [,1]     [,2]     [,3]
[1,] 6.343588 5.743588 4.910622
[2,] 6.656412 6.056412 5.089378

$out #extreme value
[1] 4.9

$group #group in which are the extreme value
[1] 1

$names #groups names
[1] "virginica"  "versicolor" "setosa"    

Box

• boxlty - box line type
• boxlwd - box line width
• boxcol - box line color
• boxfill - box fill colors

Median

• medlty - median line type ("blank" for no line)
• medlwd - median line widht
• medcol - median line color
• medpch - median point (NA for no symbol)
• medcex - median point size
• medbg - median point background color

Whisker

• whisklty - whisker line type
• whisklwd - whisker line width
• whiskcol - whisker line color

Staple

• staplelty - staple line type
• staplelwd - staple line width
• staplecol - staple line color

Outliers

• outlty - outlier line type ("blank" for no line)
• outlwd - outlier line width
• outcol - outlier line color
• outpch - outlier point type (NA for no symbol)
• outcex - outlier point size
• outbg - outlier point background color

Example

Default and heavily modified plots side by side

par(mfrow=c(1,2))
# Default
boxplot(Sepal.Length ~ Species, data=iris)
# Modified
boxplot(Sepal.Length ~ Species, data=iris,
        boxlty=2, boxlwd=3, boxfill="cornflowerblue", boxcol="darkblue",
        medlty=2, medlwd=2, medcol="red", medpch=21, medcex=1, medbg="white",
        whisklty=2, whisklwd=3, whiskcol="darkblue",
        staplelty=2, staplelwd=2, staplecol="red",
        outlty=3, outlwd=3, outcol="grey", outpch=NA
        )