Magento: All Categories and respective Thumbnails in Magento 1.9

Got it. Here is the result, we need to the attribute to the collection and then get the image from the respective folder:

<?php $_helper = Mage::helper('catalog/category'); ?>
<?php $_categories = $_helper->getStoreCategories(false, true, false)
                    //Here is the solution
                    ->addAttributeToSelect('image')                    
                    ->addOrderField('name');
 ?>
<?php if (count($_categories) > 0): ?>
    <ul>
        <?php foreach($_categories as $_category): ?>
            <li>
                <a href="<?php echo $_helper->getCategoryUrl($_category) ?>">
                    <?php 
                        echo $_category->getName();
                        echo '<img src="'$_category->getImageUrl().'" width="100" height="100"/>';
                    ?>
                </a>
            </li>
        <?php endforeach; ?>
    </ul>
<?php endif; ?>

Note: if you using Magento version less then 1.9 you change "image" to "thumbnail"

->addAttributeToSelect('thumbnail')