Use a session cookie. Could be set either via js (client side) or something like php (server-side). Here's an example of a js-only solution:
<!doctype html>
<html><head><script>
var backgrounds=['foo.png', 'bar.png', 'hahah.png'];
function setBg () {
  var currentBg=readCookie('which_bg');
  if (!currentBg) {
    currentBg=backgrounds[Math.random()*backgrounds.length|0];
    createCookie('which_bg', currentBg);
  }
  document.body.style.backgroundImage='url('+currentBg+')';
}
// from http://www.quirksmode.org/js/cookies.html
function createCookie(name,value,days) {
  if (days) {
    var date = new Date();
    date.setTime(date.getTime()+(days*24*60*60*1000));
    var expires = "; expires="+date.toGMTString();
  }
  else var expires = "";
  document.cookie = name+"="+value+expires+"; path=/";
}
function readCookie(name) {
  var nameEQ = name + "=";
  var ca = document.cookie.split(';');
  for (var i=0;i < ca.length;i++) {
    var c = ca[i];
    while (c.charAt(0)==' ') c = c.substring(1,c.length);
    if (c.indexOf(nameEQ) == 0) return c.substring(nameEQ.length,c.length);
  }
  return null;
}
function eraseCookie(name) {
  createCookie(name,"",-1);
}
</script></head>
<body onload="setBg();">
...
</body></html>