disable submit button until file selected for upload

Slightly simpler way using prop() which I think is the preferred way to do it now:

$('input:file').on("change", function() {
    $('input:submit').prop('disabled', !$(this).val()); 
});

Tested in IE, Chrome and FireFox.

If anyone is looking at this now (in 2021), this is the non-jquery solution I was able to come up with!! Some of this won't work with older browsers, so your mileage might vary- but if you're looking for a modern simple solution- this should be more than fine.

<div>
  <form method="post" action="someAction" enctype="multipart/form-data">
    <input type="file" name="fileUploaded" />
    <input type="submit" disabled="true" />
  </form>
  <script>
    document.querySelector("input[type=file]").onchange = ({
      target: { value },
    }) => {
      document.querySelector("input[type=submit]").disabled = !value;
    };
  </script>
</div>

Some notes about this solution: onChange takes a function that returns an object event, which has target and in there value. value is the string of the file name uploaded, and returns empty string when a user cancels the selection.

If you're looking for a solution that works with multiple file inputs and submissions, you can use class names to grab the right one.

<!-- index.html -->
<div>
  <form
    method="post"
    action="someAction"
    enctype="multipart/form-data"
  >
    <input class="fileUpload1" type="file" name="fileUploaded" />
    <input class="fileUpload1" type="submit" disabled="true" />
  </form>
</div>
<div>
  <form
    method="post"
    action="someOtherAction"
    enctype="multipart/form-data"
  >
    <input class="fileUpload2" type="file" name="fileUploaded2" />
    <input class="fileUpload2" type="submit" disabled="true" />
  </form>
</div>

// script.js
document.querySelectorAll("input[type=file]").forEach(
  (fileInput) =>
    (fileInput.onchange = ({ target: { value } }) => {
      document.querySelector(
        `input[type=submit].${fileInput.className}`
      ).disabled = !value;
    })
  );

Try

   $('#my_uploader').change(function() {
      if($(this).val()) {
        $('#my_submit_button').attr('disabled', '');
      } else {
        $('#my_submit_button').attr('disabled', 'disabled');
      }
    });

instead of using script simply use required in input field

If you're a fan of ternary expressions:

$(document).ready(function(){
    var $submit = $('#submit_document');
    var $file = $('#file_path');

    $file.change(
        function(){
            $submit.attr('disabled',($(this).val() ? false : true));
        }
    );
});  

Instead of disabling the submit, is it potentially more helpful to offer instruction if the user presses it without selecting a file first? So add something like this as the onclick code of the submit?

var bFileEmpty = !document.getElementById('filControl').value; if (bFileEmpty) alert('Please select a file'); return !bFileEmpty;

Note that your file control will need an ID as well as a name

A modern non-JQuery derivation of Ethan Jurman's answer, for multiple forms whose inputs are intermixed and not all within <form></form> blocks.

document.querySelectorAll("input[type=file]").forEach(
     (fileInput) =>
          (fileInput.onchange = ({target: {value}}) => {
               document.querySelector(
                    `input[form="${fileInput.form.id}"][type=submit]`
               ).disabled = !value;
          })
);

<form method="post" id="formA"></form>
<form method="post" id="formB"></form>

<input form="formA" type="file">
<input form="formA" type="submit" disabled="true">
<br>
<input form="formB" type="file">
<input form="formB" type="submit" disabled="true">

Make sure that code is not executed until the document has been loaded, or else the elements won't yet exist for it to attach the events handlers to.