Do you know about list-ability of a function? You can set that attribute to avoid explicit mapping.

SetAttributes[f, Listable];
f[{{x, y}, {a, b}}]

{{f[x], f[y]}, {f[a], f[b]}}

What about

  #^2 & /@ {{1, 2}, {3, 4}}

or

N[Sin[#]] & /@ {{1, 2}, {3, 4}}

This following command should add noise to each pixel; well actually to each of the RGB channels.

 Manipulate[
 Mod[# + RandomReal[delta, 512], 
     1] & /@ (ExampleData[{"TestImage", "Lena"}] // ImageData) // 
  Image, {delta, 0, 0.5}]

This gives:

A much more interesting example is given in this fantastic blog post: Doing spy stuff with Mathematica.

M.