Dynamically Changing CSS Background Image

Made a few amendments to your code

DEMO: http://jsfiddle.net/p77KW/

var header = $('body');

var backgrounds = new Array(
    'url(http://placekitten.com/100)'
  , 'url(http://placekitten.com/200)'
  , 'url(http://placekitten.com/300)'
  , 'url(http://placekitten.com/400)'
);

var current = 0;

function nextBackground() {
    current++;
    current = current % backgrounds.length;
    header.css('background-image', backgrounds[current]);
}
setInterval(nextBackground, 1000);

header.css('background-image', backgrounds[0]);

Biggest changes (as noted in others comments) is that you have to use apostrophe**'**s, not those funky open and close single-quotes and that your array wasn't correct.

With these corrections out of the way I simplified a few things:

1. Increment current then take modulus (I know this is basically what you did but how much easier is that to debug ;))
2. Target background-image directly
3. Used setInterval() instead of a double call to setTimeout

You could acheive this same technique with HTML/CSS Only by 1. placing images within an "img" tag in your HTML surrounded by a "div wrapper" and setting it to position:relative and div wrapper img's to position:absolute. For full-width/full-height you can use percentages or potentially "background-size:cover" (haven't checked) and then call a CSS animation to change the images dynamically.

Or 2. you can add multiple images to a background in your CSS separated by commas, apply background-size:cover and again use CSS animations to change the background.

Here's an example and also Mozilla CSS3 Animation Documentation