CSS - How to center nested divs?

You could use relative positioning:

http://jsfiddle.net/a879W/

#formpanel {
    position: relative;
    ...
}

#loginForm {
    position: absolute;
    top: 50%;
    left: 50%;
    margin-top: -100px;
    margin-left: -100px;
    width: 200px;
    height: 200px;
    background-color:blue;
}

#loginForm {
  position:absolute;
  top:25%;
  margin: auto;
  width: 50%;
  height: 50%;
  background-color:blue;
}

EDIT: top: 25% not 50%.