We had need of a combobox at work and after looking around at the available options I was not happy with any of them. The project had all it's styling based on Twitter's Bootstrap, so building on that made sense.
The dependencies are the Bootstrap stylesheet(CSS or LESS) and also the typeahead javascript plugin. Include them and then the stylesheet(CSS or LESS) and javascript.
Then just activate the plugin on a normal select box(suggest having a blank option first):
<select class="combobox">
<option></option>
<option value="PA">Pennsylvania</option>
<option value="CT">Connecticut</option>
<option value="NY">New York</option>
<option value="MD">Maryland</option>
<option value="VA">Virginia</option>
</select>
<script type="text/javascript">
$(document).ready(function(){
$('.combobox').combobox();
});
</script>