How to make a DIV always float on the screen in top right corner?

Use position: fixed, and anchor it to the top and right sides of the page:

#fixed-div {
    position: fixed;
    top: 1em;
    right: 1em;
}

IE6 does not support position: fixed, however. If you need this functionality in IE6, this purely-CSS solution seems to do the trick. You’ll need a wrapper <div> to contain some of the styles for it to work, as seen in the stylesheet.