Why does returning false in the keydown callback does not stop the button click event?

Hope this answers your question:

<input type="button" value="Press" onkeydown="doOtherStuff(); return false;">

return false; successfully cancels an event across browsers if called at the end of an event handler attribute in the HTML. This behaviour is not formally specified anywhere as far as I know.

If you instead set an event via an event handler property on the DOM element (e.g. button.onkeydown = function(evt) {...}) or using addEventListener/attachEvent (e.g. button.addEventListener("keydown", function(evt) {...}, false)) then just returning false from that function does not work in every browser and you need to do the returnValue and preventDefault() stuff from my other answer. preventDefault is specified in the DOM 2 spec and is implemented by most mainstream modern browsers. returnValue is IE-specific.

First, if you're detecting a printable character such as space, you would be better off with the keypress event. Secondly, the way to prevent the default action is to call preventDefault() on the event in non-IE browsers and set the event's returnValue property to false in IE.

var button = document.getElementById("button");
button.onkeypress = function(evt) {
   evt = evt || window.event;
   var charCode = evt.keyCode || evt.which;
   if (charCode == 32) {
       if (evt.preventDefault) {
           evt.preventDefault();
       } else {
           evt.returnValue = false;
       }
   }
};

I'm not a jQuery expert and I assume it takes care of obtaining the event for you:

$("button").keypress(function(evt) {
   var charCode = evt.keyCode || evt.which;
   if (charCode == 32) {
       if (evt.preventDefault) {
           evt.preventDefault();
       } else {
           evt.returnValue = false;
       }
   }
});