You want to use point shapes that are different from the defaults.

If you want to set the shape of all the points (Figure 5-6), specify the shape in geom_point():

library(gcookbook) # For the data set

ggplot(heightweight, aes(x=ageYear, y=heightIn)) + geom_point(shape=3)

Figure 5-6. Left: scatter plot with the shape aesthetic set to a custom value; right: with a variable mapped to shape, using a custom shape palette

If you have mapped a variable to shape, use scale_shape_manual() to change the shapes:

# Use slightly larger points and use a shape scale with custom values
ggplot(heightweight, aes(x=ageYear, y=heightIn, shape=sex)) +
    geom_point(size=3) + scale_shape_manual(values=c(1, 4))