As rcs stated, cex will do the job in base graphics package. I reckon that you're not willing to do your graph in ggplot2 but if you do, there's a size aesthetic attribute, that you can easily control (ggplot2 has user-friendly function arguments: instead of typing cex (character expansion), in ggplot2 you can type e.g. size = 2 and you'll get 2mm point).
Here's the example:
### base graphics ###
plot(mpg ~ hp, data = mtcars, pch = 16, cex = .9)
### ggplot2 ###
# with qplot()
qplot(mpg, hp, data = mtcars, size = I(2))
# or with ggplot() + geom_point()
ggplot(mtcars, aes(mpg, hp), size = 2) + geom_point()
# or another solution:
ggplot(mtcars, aes(mpg, hp)) + geom_point(size = 2)