From ggplot2 2.0.0 you can use the margin = argument of element_text() to change the distance between the axis title and the numbers. Set the values of the margin on top, right, bottom, and left side of the element.
ggplot(mpg, aes(cty, hwy)) + geom_point()+
theme(axis.title.y = element_text(margin = margin(t = 0, r = 20, b = 0, l = 0)))
margin can also be used for other element_text elements (see ?theme), such as axis.text.x, axis.text.y and title.
addition
in order to set the margin for axis titles when the axis has a different position (e.g., with scale_x_...(position = "top"), you'll need a different theme setting - e.g. axis.title.x.top. See https://github.com/tidyverse/ggplot2/issues/4343.