EDIT : this answer used to claim that it isn't possible to center an absolutely positioned element with margin: auto;, but this simply isn't true. Because this is the most up-voted and accepted answer, I guessed I'd just change it to be correct.
When you apply the following CSS to an element
position: absolute;
top: 0;
left: 0;
right: 0;
bottom: 0;
margin: auto;
And then give the element a fixed width and height, such as 200px or 40%, the element will center itself.
Here's a Fiddle that demonstrates the effect.