As @pimvdb said in his comment,
Note that change will only fire when the input element has lost focus.
There is also the input event which fires whenever the textbox updates
without it needing to lose focus. Unlike key events it also works for
pasting/dragging text.
(See documentation.)
This is so useful, it is worth putting it in an answer. Currently (v1.8*?) there is no .input() convenience fn in jquery, so the way to do it is
$('input.myTextInput').on('input',function(e){
alert('Changed!')
});