How to show Category List in Magento

You can show all categories present in magento.
There are different methods to get the category list. Below are some possible methods:-
Get all categories
The following code will fetch all categories (both active and inactive) that are present in your Magento Shop.

$categories = Mage::getModel('catalog/category')
                    ->getCollection()
                    ->addAttributeToSelect('*');

Get all active categories:
The following code will fetch all active categories that are present in your Magento Shop. Thus filtering the inactive categories.

$categories = Mage::getModel('catalog/category')
                    ->getCollection()
                    ->addAttributeToSelect('*')
                  ->addIsActiveFilter();

Get active categories of any particular level:
The following code will fetch all active categories of certain/specific level. Here, I have chosen level 1. Also sorting categories by name.

$categories = Mage::getModel('catalog/category')
                    ->getCollection()
                    ->addAttributeToSelect('*')
                    ->addIsActiveFilter()
                    ->addLevelFilter(1)
                    ->addOrderField('name');

Get store specific categories:
The following code will fetch all active store specific categories. The following helper function does so:-

getStoreCategories($sorted=false, $asCollection=false, $toLoad=true)
$helper = Mage::helper('catalog/category'); 
// sorted by name, fetched as collection
$categoriesCollection = $helper->getStoreCategories('name', true, false); 
// sorted by name, fetched as array
$categoriesArray = $helper->getStoreCategories('name', false, false);