Edit
Okay, from your description it sounds like you want to get the child categories from the current category you're in. (I.E. Get cups
and plates
while in batman
category view).
The following should be just about as little as you need to get the current children.
<?php
$_helper = Mage::helper('catalog/category');
$children = Mage::registry( 'current_category' )->getChildrenCategories();
?>
<ul>
<?php foreach( $children as $child ): ?>
<li><a href="<?php echo $_helper->getCategoryUrl($child); ?>"><?php echo $child->getName() ?></a></li>
<?php endforeach; ?>
</ul>
Previous Answer(s)
It's a little roundabout, but this can get you the parent category id from a product object.
//If you don't have a product to start with, load by ID.
$_product = Mage::getModel( 'catalog/product' )->load($id);
//Assign Category Model
$categoryModel = Mage::getModel( 'catalog/category' );
//Get Array of Category Id's with Last as First (Reversed)
$_categories = array_reverse( $_product->getCategoryIds() );
//Get Parent Category Id
$_parentId = $categoryModel->load($_categories[0])->getParentId();
//Load Parent Category
$_category = $categoryModel->load($_parentId);
//Do something with $_category
echo $_category->getName();
It works better when the product only has one category Id assigned to it. You may not get the category you want if multiple categories have been assigned to that one product.
Also, you can get it a slightly quicker way, but this method doesn't work if the product was searched for:
$_category = Mage::getModel( 'catalog/category' )->load( Mage::registry( 'current_category' )->getParentId() );
I didn't test the line above, but it should work. Only if the product was reached by browsing through the categories though.