How to get the mouse position without events (without moving the mouse)?

Real answer: No, it's not possible.

OK, I have just thought of a way. Overlay your page with a div that covers the whole document. Inside that, create (say) 2,000 x 2,000 <a> elements (so that the :hover pseudo-class will work in IE 6, see), each 1 pixel in size. Create a CSS :hover rule for those <a> elements that changes a property (let's say font-family). In your load handler, cycle through each of the 4 million <a> elements, checking currentStyle / getComputedStyle() until you find the one with the hover font. Extrapolate back from this element to get the co-ordinates within the document.

N.B. DON'T DO THIS.

What you can do is create variables for the x and y coordinates of your cursor, update them whenever the mouse moves and call a function on an interval to do what you need with the stored position.

The downside to this of course is that at least one initial movement of the mouse is required to have it work. As long as the cursor updates its position at least once, we are able to find its position regardless of whether it moves again.

var cursor_x = -1;
var cursor_y = -1;
document.onmousemove = function(event)
{
 cursor_x = event.pageX;
 cursor_y = event.pageY;
}
setInterval(check_cursor, 1000);
function check_cursor(){console.log('Cursor at: '+cursor_x+', '+cursor_y);}

The preceding code updates once a second with a message of where your cursor is. I hope this helps.

Edit 2020: This does not work any more. It seems so, that the browser vendors patched this out. Because the most browsers rely on chromium, it might be in its core.

Old answer: You can also hook mouseenter (this event is fired after page reload, when the mousecursor is inside the page). Extending Corrupted's code should do the trick:

var x = null;
var y = null;
    
document.addEventListener('mousemove', onMouseUpdate, false);
document.addEventListener('mouseenter', onMouseUpdate, false);
    
function onMouseUpdate(e) {
  x = e.pageX;
  y = e.pageY;
  console.log(x, y);
}

function getMouseX() {
  return x;
}

function getMouseY() {
  return y;
}

You can also set x and y to null on mouseleave-event. So you can check if the user is on your page with it's cursor.