This example widget code, place the code in separate file, then include it in finctions.php like that:

require( get_template_directory() . '/menu-widget.php' );

Register the widget(match the class names!)-

    function register_my_widget() {  
        register_widget( 'example_widget' );  
    }  

And call the widget:

add_action( 'widgets_init', function(){
     register_widget( 'My_Widget' );
});

And here it comes the widget code:

<?php
/**
 * Example Widget Class
 */
class example_widget extends WP_Widget {
 
 
    /** constructor -- name this the same as the class above */
    function example_widget() {
        parent::WP_Widget(false, $name = 'Example Text Widget');	
    }
 
    /** @see WP_Widget::widget -- do not rename this */
    function widget($args, $instance) {	
        extract( $args );
        $title 		= apply_filters('widget_title', $instance['title']);
        $message 	= $instance['message'];
        ?>
              <?php echo $before_widget; ?>
                  <?php if ( $title )
                        echo $before_title . $title . $after_title; ?>
							<ul>
								<li><?php echo $message; ?></li>
							</ul>
              <?php echo $after_widget; ?>
        <?php
    }
 
    /** @see WP_Widget::update -- do not rename this */
    function update($new_instance, $old_instance) {		
		$instance = $old_instance;
		$instance['title'] = strip_tags($new_instance['title']);
		$instance['message'] = strip_tags($new_instance['message']);
        return $instance;
    }
 
    /** @see WP_Widget::form -- do not rename this */
    function form($instance) {	
 
        $title 		= esc_attr($instance['title']);
        $message	= esc_attr($instance['message']);
        ?>
         <p>
          <label for="<?php echo $this->get_field_id('title'); ?>"><?php _e('Title:'); ?></label> 
          <input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo $title; ?>" />
        </p>
		<p>
          <label for="<?php echo $this->get_field_id('message'); ?>"><?php _e('Simple Message'); ?></label> 
          <input class="widefat" id="<?php echo $this->get_field_id('message'); ?>" name="<?php echo $this->get_field_name('message'); ?>" type="text" value="<?php echo $message; ?>" />
        </p>
        <?php 
    }
 
 
} // end class example_widget
add_action('widgets_init', create_function('', 'return register_widget("example_widget");'));
?>

You can use ultimate posts widget to display posts – ultimate-posts-widget.1.8.1