Cacher is the code snippet organizer for pro developers

<?php
//http://clicknathan.com/web-design/wordpress-custom-taxonomy-dropdown-without-a-submit-button/
//This goes function.php
class my_Walker_CategoryDropdown extends Walker_CategoryDropdown {

	function start_el(&$output, $category, $depth, $args) {
		$pad = str_repeat(' ', $depth * 3);

		$cat_name = apply_filters('list_cats', $category->name, $category);
		$output .= "\t<option class=\"level-$depth\" value=\"".$category->slug."\"";
		if ( $category->term_id == $args['selected'] )
			$output .= ' selected="selected"';
		$output .= '>';
		$output .= $pad.$cat_name;
		if ( $args['show_count'] )
			$output .= '  ('. $category->count .')';
		if ( $args['show_last_update'] ) {
			$format = 'Y-m-d';
			$output .= '  ' . gmdate($format, $category->last_update_timestamp);
		}
		$output .= "</option>\n";
	}
}


//This goes where you want the form input to appear - change to your taxonomy slug in 2 locations
<form method="get" action="/">
	<fieldset>

		<?php $args = array(
			'show_option_all'    => 'Choose one...',
			'taxonomy'           => 'YOUR-TAXONOMY-SLUG',
			'orderby'            => 'name',
			'walker' => new my_Walker_CategoryDropdown
		);

		wp_dropdown_categories( $args ); ?>
		<script type="text/javascript"><!--
		    var dropdown = document.getElementById("cat");
		    function onCatChange() {
				if ( dropdown.options[dropdown.selectedIndex].value != '0' ) {
					location.href = "<?php echo get_option('home');
		?>/?YOUR-TAXONOMY-SLUG="+dropdown.options[dropdown.selectedIndex].value;
				}
		    }
		    dropdown.onchange = onCatChange;
		--></script> 

	</fieldset>
</form>