[JsLoveR]

Если прямоугольники параллельны осям.

<script type="text/javascript">

window.onload = function() {
	
	var box1 = document.getElementById("box1");
	var box2 = document.getElementById("box2");
	
	function rect2Rect(obj1, obj2) {
	   return ( obj1.offsetLeft <= obj2.offsetLeft + obj2.offsetWidth && obj1.offsetLeft + obj1.offsetWidth  >=  obj2.offsetLeft && obj1.offsetTop + obj1.offsetHeight >=  obj2.offsetTop && obj1.offsetTop <= obj2.offsetTop +  obj2.offsetHeight );
	}

	function move() {
	   if(!rect2Rect(box1, box2)) {
	     setTimeout(function() {
		   box1.style.left = box1.offsetLeft + 5 + "px";
		   box2.style.top = box2.offsetTop - 5 + "px";
		   move();
	     }, 50);
	   }
	   else{
	     alert("Столкновение");
	   }
	}
	move();
}
</script>

<div id="box1" style=" width:30px; height:30px; background-color:#0099FF; position:absolute; left:10px"></div>
<div id="box2" style=" width:30px; height:30px; background-color:#CCCC00; position:absolute; left:100px; top:100px; "></div>