This layout override tutorial gives you a basis for overriding the output of the Joomla banners module. This simple example shows you how to add a title tag to the click link but also gives you a base for allowing addition customisation.

The banner module is a little difficult to override because much of it's output logic is hidden in a helper method.  The first step in creating this override is to copy:

/modules/mod_banners/tmpl/default.php

to:

/templates/your_template/html/mod_banners/default.php

Then replace the code in the new file with the following:

<?php // no direct access
defined('_JEXEC') or die('Restricted access');
$baseurl = JURI::base();
?>
<div class="bannergroup<?php echo $params->get('moduleclass_sfx') ?>">
<?php if ($headerText) : ?>
    <div class="bannerheader"><?php echo $headerText ?></div>
<?php endif; ?>

<?php foreach($list as $item) :
    $link = JRoute::_('index.php?option=com_banners&task=click&bid='. $item->bid);
?>
    <div class="banneritem<?php echo $params->get('moduleclass_sfx') ?>">
    <?php
        if (trim($item->custombannercode)) :
            // Text based banners
            echo str_replace(
                array('{CLICKURL}', '{NAME}'),
                array($link, $item->name),
                $item->custombannercode
            );
        elseif (BannerHelper::isImage($item->imageurl)) :
            // Image based banner
            if ($item->clickurl) :
                $target = $params->get('target', 1);
                // Wrap the banner in a link
                if ($target == 1) :
                    // Open in a new window
            ?>
            <a href="<?php echo $link; ?>" target="_blank"
                title="<?php echo htmlspecialchars($item->name, ENT_QUOTES, 'UTF-8');?>">
                <img src="<?php echo $baseurl;?>images/banners/<?php echo $item->imageurl;?>"
                    alt="<?php echo JText::_('Banner');?>" /></a>

            <?php
                elseif ($target == 2):
                    // open in a popup window
            ?>
            <a href="javascript:void window.open('<?php echo $link;?>', '',
                'toolbar=no,location=no,status=no,menubar=no,scrollbars=yes,resizable=yes,width=780,height=550'); return false"
                title="<?php echo htmlspecialchars($item->name, ENT_QUOTES, 'UTF-8');?>">
                <img src="<?php echo $baseurl;?>images/banners/<?php echo $item->imageurl;?>"
                    alt="<?php echo JText::_('Banner');?>" /></a>
            <?php
                else :
                    // open in parent window
            ?>
            <a href="<?php echo $link;?>"
                 title="<?php echo htmlspecialchars($item->name, ENT_QUOTES, 'UTF-8');?>">
                <img src="<?php echo $baseurl;?>images/banners/<?php echo $item->imageurl;?>"
                    alt="<?php echo JText::_('Banner');?>" /></a>
            <?php
                endif;
            else :
                // Just display the image if no link specified
            ?>
                <img src="<?php echo $baseurl;?>images/banners/<?php echo $item->imageurl;?>"
                    alt="<?php echo JText::_('Banner');?>" /></a>
            <?php
            endif;
        elseif (BannerHelper::isFlash($item->imageurl)) :
            //echo $item->params;
            $params2 = new JParameter($item->params);
            $width = $params2->get('width');
            $height = $params2->get('height');
            $imageurl = $baseurl."images/banners/".$item->imageurl;
        ?>
        <object classid="clsid:D27CDB6E-AE6D-11cf-96B8-444553540000"
                codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=6,0,0,0"
                border="0"
                width="<?php echo $width;?>"
                height="<?php echo $height;?>">
            <param name="movie" value="<?php echo $imageurl;?>" />
            <embed src="<?php echo $imageurl;?>"
                    loop="false"
                    pluginspage="http://www.macromedia.com/go/get/flashplayer"
                    type="application/x-shockwave-flash"
                    width="<?php echo $width;?>"
                    height="<?php echo $height;?>">
            </embed>
        </object>";
        <?php
        endif;
    ?><div class="clr"></div>
    </div>
<?php endforeach; ?>

<?php if ($footerText) : ?>
    <div class="bannerfooter<?php echo $params->get('moduleclass_sfx') ?>">
         <?php echo $footerText ?>
    </div>
<?php endif; ?>
</div>

You can obviously see that there is a lot more code than in the original layout.  This is because I've imported all of the code in the helper.

All I've really done here is add a title tag to the link tag because I wanted a descriptive title to display when someone hovered over the banners on this site (see the Rochen banner and the images under the "Thanks to" heading).  However, this also gives you a basis for customising the banner module, particularly if you haven't been able to work out how.  You could also provide a more informative alt tag in the image if this was useful for your site.

You can download the layout overrides shown from joomlacode.org: mod_banners_layout_override.zip.  To install them, unzip the files into the /html/ folder in your default Joomla template.  Remember to backup any files and folders that already exist (just in case).

For more information on Joomla layout overrides, see my tutorial here.