Can jQuery check whether input content has changed?

There is a simple solution, which is the HTML5 input event. It's supported in current versions of all major browsers for <input type="text"> elements and there's a simple workaround for IE < 9. See the following answers for more details:

• jQuery keyboard events
• Catch only keypresses that change input?

Example (except IE < 9: see links above for workaround):

$("#your_id").on("input", function() {
    alert("Change to " + this.value);
});

Yes, compare it to the value it was before it changed.

var previousValue = $("#elm").val();
$("#elm").keyup(function(e) {
    var currentValue = $(this).val();
    if(currentValue != previousValue) {
         previousValue = currentValue;
         alert("Value changed!");
    }
});

Another option is to only trigger your changed function on certain keys. Use e.KeyCode to figure out what key was pressed.