You have to create a copy of the app/design/frontend/base/default/template/page/switch/stores.phtml template in your custom theme package.

Then you have to modify it to use the following code:

<?php
$websites = Mage::app()->getWebsites();

if (count($websites) > 1): ?>
<div class=”website-switcher”>
    <label for=”select-website”><?php echo $this->__(‘Select Store:’) ?></label>
    <select id=”select-website” title=”<?php echo $this->__(‘Select Store’) ?>” onchange=”location.href=this.value”>
    <?php foreach ($websites as $website): // print out each website name and code as a dropdown box item ?>
        <?php $_selected = $website->getCode() == Mage::app()->getWebsite()->getCode() ? ‘ selected=”selected”‘ : ” ?>
        <option value=”<?php echo $website->getDefaultStore()->getBaseUrl()?>”<?php echo $_selected ?>><?php echo $this->htmlEscape($website->getName()) ?></option>
    <?php endforeach; ?>
    </select>
</div>
<?php endif; ?>

Links to Magento API docs for the methods used:

• Mage::app()->getWebsites()
• Mage::app()->getWebsite()->getCode()
• $website->getCode()
• $website->getDefaultStore()->getBaseUrl()