/* image SEO reminder class
 by serge liatko
 updated version 0.3
*/
class image_seo_reminder {
	private $allowed = array(
		'a' => array(
			'class' => array(),
			'href' => array(),
			'rel' => array(),
			'title' => array(),
			'target' => array()),
		'span' => array(
			'class' => array(),
			'title' => array()),
		'em' => array(),
		'strong' => array(),
		'u' => array(),
		'code' => array(),
		'sup' => array(),
		'sub' => array(),
		'cite' => array(),
		'strike' => array(),
		'br' => array()
	);
	public function __construct() {
		add_action('admin_init',array($this,'admin_init'),99,0);
	}
	public function admin_init() {
		add_filter( "manage_media_columns", array($this,'img_columns'),10,1);
		add_action('manage_media_custom_column',array($this,'print_img_columns'),10,2);
	}
	public function img_columns($columns) {
		$columns['image_alt'] = __('Alternative Text');
		$columns['post_excerpt'] = __('Caption');
		return $columns;
	}
	public function print_img_columns($name, $post_id) {
		$attachment = get_post($post_id);
		if(!is_object($attachment) || is_wp_error($attachment)) return;
		if(substr($attachment->post_mime_type, 0, 5) == 'image') {
			switch($name) {
				case 'image_alt' :
					$none = '<span style="color:#dd0000;">'. __('Empty') .'</span>';
					$alt = stripslashes(get_post_meta($post_id, '_wp_attachment_image_alt', true ));
					echo !empty($alt) ? $alt : $none;
				break;

				case 'post_excerpt' :
					echo (!empty($attachment->post_excerpt)) ? trim(wptexturize(wp_kses(stripslashes($attachment->post_excerpt), $this->allowed))) : '' ;
				break;
			}
		}
	}
}
$image_seo_reminder = new image_seo_reminder ;

which is great as adds extra columns on media library screen that tells (in red) "empty" when user has forgotten to add alternative text

http://core.trac.wordpress.org/ticket/21176 was resolved.

/* image SEO reminder class
 by serge liatko
 updated version 0.2
*/
class image_seo_reminder {
	private $allowed = array(
		'a' => array(
			'class' => array(),
			'href' => array(),
			'rel' => array(),
			'title' => array(),
			'target' => array()),
		'span' => array(
			'class' => array(),
			'title' => array()),
		'em' => array(),
		'strong' => array(),
		'u' => array(),
		'code' => array(),
		'sup' => array(),
		'sub' => array(),
		'cite' => array(),
		'strike' => array(),
		'br' => array()
	);
	public function __construct() {
		add_action('admin_init',array($this,'admin_init'),99,0);
	}
	public function admin_init() {
		add_filter("attachment_fields_to_edit", array($this,"alt_text_field_reminder"), 15, 1);
		add_filter( "manage_media_columns", array($this,'img_columns'),10,1);
		add_action('manage_media_custom_column',array($this,'print_img_columns'),10,2);
	}
	public function img_columns($columns) {
		$columns['image_alt'] = __('Alternate Text');
		$columns['post_excerpt'] = __('Caption');
		return $columns;
	}
	public function print_img_columns($name, $post_id) {
		$attachment = get_post($post_id);
		if(!is_object($attachment) || is_wp_error($attachment)) return;
		if(substr($attachment->post_mime_type, 0, 5) == 'image') {
			switch($name) {
				case 'image_alt' :
					$none = '<span style="color:#dd0000;">'. __('Empty') .'</span>';
					$alt = stripslashes(get_post_meta($post_id, '_wp_attachment_image_alt', true ));
					echo !empty($alt) ? $alt : $none;
				break;

				case 'post_excerpt' :
					echo (!empty($attachment->post_excerpt)) ? trim(wptexturize(wp_kses(stripslashes($attachment->post_excerpt), $this->allowed))) : '' ;
				break;
			}
		}
	}
	public function alt_text_field_reminder($form_fields) {
		if (isset($form_fields['image_alt']) && is_array($form_fields['image_alt']) && isset($form_fields['image_alt']['helps'])) {
			$form_fields['image_alt']['helps'] = __('Alt text is <strong>mandatory</strong> if you care about SEO of your website!','ewpfi_lang') . '&nbsp;<a href="http://wordpress.org/extend/ideas/topic/auto-populate-alternative-text-to-match-title-unless-otherwise-specified/" target="_blank">'. __('Read More') .'</a>';
			$form_fields['image_alt']['required'] = true;
		}
		return $form_fields;
	}
}
$image_seo_reminder = new image_seo_reminder ;

/* image SEO reminder */
class image_seo_reminder {
	private $allowed = array(
		'a' => array(
			'class' => array(),
			'href' => array(),
			'rel' => array(),
			'title' => array(),
			'target' => array()),
		'span' => array(
			'class' => array(),
			'title' => array()),
		'em' => array(),
		'strong' => array(),
		'u' => array(),
		'code' => array(),
		'sup' => array(),
		'sub' => array(),
		'cite' => array(),
		'strike' => array(),
		'br' => array()
	);
	public function __construct() {
		add_action('admin_init',array($this,'admin_init'),99,0);
	}
	public function admin_init() {
		add_filter("attachment_fields_to_edit", array($this,"alt_text_field_reminder"), 15, 1);
		add_filter( "manage_media_columns", array($this,'img_columns'),10,1);
		add_action('manage_media_custom_column',array($this,'print_img_columns'),10,2);
	}
	public function img_columns($columns) {
		$columns['image_alt'] = __('Alternate Text');
		$columns['post_excerpt'] = __('Caption');
		return $columns;
	}
	public function print_img_columns($name, $post_id) {
		$none = '<span style="color:#dd0000;">'. __('Empty') .'</span>';
		switch($name) {
			case 'image_alt' :
				$alt = stripslashes(get_post_meta($post_id, '_wp_attachment_image_alt', true ));
				echo !empty($alt) ? $alt : $none;
			break;

			case 'post_excerpt' :
				$attachment = get_post($post_id);
				if(!is_object($attachment) || is_wp_error($attachment)) break;
				echo (!empty($attachment->post_excerpt)) ? trim(wptexturize(wp_kses(stripslashes($attachment->post_excerpt), $this->allowed))) : '' ;
			break;
		}
	}
	public function alt_text_field_reminder($form_fields) {
		if (isset($form_fields['image_alt']) && is_array($form_fields['image_alt']) && isset($form_fields['image_alt']['helps'])) {
			$form_fields['image_alt']['helps'] = $form_fields['image_alt']['helps'] . '<br /><abbr title="required" class="required">*</abbr>&nbsp;' . __('Alt text is actually <strong>mandatory</strong> if you care about SEO of your website!','ewpfi_lang');
		}
		return $form_fields;
	}
}
$image_seo_reminder = new image_seo_reminder ;

There is no ALT tag like <alt>...</alt>. There is the alt attribute some HTML elements like IMG have. I don't no how it comes to write about the "alt tag for images". In this case the alt attribute of IMG-elements is meant.

The alt attribute is not the same as the title attribute, see the HTML specs.