You're looking for bounding box collision detection. If you want to raise an event, you have to repeatedly test, but it would be better just to run the function over all your game objects from your game loop. The sandbox is at http://jsfiddle.net/nGRwt/7/

  function collision($div1, $div2) {
      var x1 = $div1.offset().left;
      var y1 = $div1.offset().top;
      var h1 = $div1.outerHeight(true);
      var w1 = $div1.outerWidth(true);
      var b1 = y1 + h1;
      var r1 = x1 + w1;
      var x2 = $div2.offset().left;
      var y2 = $div2.offset().top;
      var h2 = $div2.outerHeight(true);
      var w2 = $div2.outerWidth(true);
      var b2 = y2 + h2;
      var r2 = x2 + w2;

      if (b1 < y2 || y1 > b2 || r1 < x2 || x1 > r2) return false;
      return true;
    }

You can try jquery-collision plus jquery-ui-draggable-collision. Full disclosure: I just wrote and released these on sourceforge.

The first allows this:

var hit_list = $("#collider").collision(".obstacle");

which is the list of all ".obstacle" that overlap "#collider".

The second allows:

$("#collider").draggable( { obstacle: ".obstacle" } );

Which gives you (among other things), a "collision" event to bind to:

$("#collider").bind( "collision", function(event,ui){...} );

And you can even set:

$("#collider").draggable( { obstacle: ".obstacle", preventCollision: true } );

to prevent "#collider" from ever overlapping any ".obstacle" while dragging.

in Native Javascript

var is_colliding = function(div1, div2) {
  var d1_height = div1.offsetHeight;
  var d1_width = div1.offsetWidth;
  var d1_distance_from_top = div1.offsetTop + d1_height;
  var d1_distance_from_left = div1.offsetLeft + d1_width;

  var d2_height = div2.offsetHeight;
  var d2_width = div2.offsetWidth;
  var d2_distance_from_top = div2.offsetTop + d2_height;
  var d2_distance_from_left = div2.offsetLeft + d2_width;

  var not_colliding =
    d1_distance_from_top < div2.offsetTop ||
    div1.offsetTop > d2_distance_from_top ||
    d1_distance_from_left < div2.offsetTop ||
    div1.offsetLeft > d2_distance_from_left;

  return !not_colliding;
};