< ?php wp_dropdown_categories(); ?>

$defaults = array('show_option_all' => '', 'show_option_none' => '', 'orderby' => 'ID',
    'order' => 'ASC', 'show_last_update' => 0, 'show_count' => 0, 'hide_empty' => 1,
    'child_of' => 0, 'exclude' => '', 'echo' => 1, 'selected' => 0, 'hierarchical' => 0,
    'name' => 'cat', 'class' => 'postform', 'depth' => 0);

<li id="categories">
         <h2>< ?php _e('Categories:'); ?></h2>
             <form action="<?php bloginfo('url'); ?>" method="get">
            < ?php wp_dropdown_categories('show_count=1&hierarchical=1'); ?>
            <input type="submit" name="submit" value="view" />
             </form>
          </li>

<li id="categories"><h2>< ?php _e('Posts by Category'); ?></h2>
          < ?php wp_dropdown_categories('show_option_none=Select category'); ?>        
          <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');
          ?>/?cat="+dropdown.options[dropdown.selectedIndex].value;
        }
             }
            dropdown.onchange = onCatChange;
        --></script>
        </li>

<li id="categories">
         <h2>< ?php _e('Posts by Category'); ?></h2>
         <form action="<?php bloginfo('url'); ?>/" method="get">
         < ?php
         $select = wp_dropdown_categories('show_option_none=Select category&show_count=1&orderby=name&echo=0');
         $select = preg_replace("#<select([^>]*)>#", "<select $1 onchange='return this.form.submit()'>", $select);
         echo $select;
         ?>
         <noscript><input type="submit" value="View" /></noscript>
         </select></form>
         </li>