Using base graphics, the standard way to do this is to use axes=FALSE, then create your own axes using Axis (or axis). For example,
x <- 1:20
y <- runif(20)
plot(x, y, axes=FALSE, frame.plot=TRUE)
Axis(side=1, labels=FALSE)
Axis(side=2, labels=FALSE)
The lattice equivalent is
library(lattice)
xyplot(y ~ x, scales=list(alternating=0))