Add value to a drop down menu with a form
<form>
  <select name="users" onchange="showUser(this.value)">
    <option value="">Select a category:</option>
    <option value="movie">Movie</option>
    <option value="musik">Musik</option>
    <option value="books">Books</option>
    <option value="images">Images</option>
  </select>
</form>

<form>
    <select id="categories" name="users" onchange="showUser(this.value)">
    <option value="">Select a category:</option>
    <option value="movie">Movie</option>
    <option value="musik">Musik</option>
    <option value="books">Books</option>
    <option value="images">Images</option>
    </select>
    </form>​​

var categories = document.getElementById("categories");

var newOption = document.createElement('option');
newOption.innerText = "New value";
newOption.setAttribute('value', 'newvalue');

categories.appendChild(newOption);
​

$("#categories").append("<option value='newvalue'>New Value</option>");

<select id="mySelect"></select>
<p>&nbsp;</p>
<input type="text" id="string"><br>
<button id="append">Append</button>


$('#append').click(function(){
    var str = $('#string').val();
    var substr = str.split(', ');
    $('#mySelect').append( new Option(substr[0],substr[1]));
});