Generate Category Tree Recursively

The code is given below, will explain the code line by line

<?php 
$rootcatId= Mage::app()->getStore()->getRootCategoryId(); 
$categories = Mage::getModel('catalog/category')->getCategories($rootcatId);
function  get_categories($categories) {
    $array= '<ul>';
    foreach($categories as $category) {
       	$cat = Mage::getModel('catalog/category')->load($category->getId());
    	$count = $cat->getProductCount();
        $array .= '<li>'.
        '<a href="' . Mage::getUrl($cat->getUrlPath()). '">' . 
                  $category->getName() . "(".$count.")</a>\n";
        if($category->hasChildren()) {
            $children = Mage::getModel('catalog/category')->getCategories($category->getId());
             $array .=  get_categories($children);
            }
         $array .= '</li>';
    }
    return  $array . '</ul>';
}
echo  get_categories($categories); ?>

Explanation of the code step by step:

  $rootcatId= Mage::app()->getStore()->getRootCategoryId(); 

This function gives return the Root Catalog Id of your current store. Usually the value is 2 but its always better to use this function.

$categories = Mage::getModel('catalog/category')->getCategories($rootcatId);

This function returns all sub categories of the parent category. This function is defined in Mage_Catalog_Model_Category. the definition is

/**
     * Retrieve categories by parent
     *
     * @param int $parent
     * @param int $recursionLevel
     * @param bool $sorted
     * @param bool $asCollection
     * @param bool $toLoad
     * @return mixed
     */
    public function getCategories($parent, $recursionLevel = 0, $sorted=false, $asCollection=false, $toLoad=true);

function  get_categories($categories) { //This is the recursive function created and here we pass the a collection of categories.
$array= '<ul>';  //$array is a variable to store all the category detail .
foreach($categories as $category) {
     	$cat = Mage::getModel('catalog/category')->load($category->getId());
        $count = $cat->getProductCount(); //$count the total no of products in the category
        $array .= '<li>'.'<a href="' . Mage::getUrl($cat->getUrlPath()). '">' . $category->getName() . "(".$count.")</a>\n"; //In this line we get an a link for the product and product count of that category
        if($category->hasChildren()) {  if category has children or not. If yes then it proceed in inside loop.
        	 $children = Mage::getModel('catalog/category')->getCategories($category-> getId()); // $children get a list of all subcategories
            $array .=  get_categories($children); //recursive call the get_categories function again.
            }
         $array .= '</li>';
    }
    return  $array . '</ul>';
}
echo  get_categories($categories); //echo all categories in the website, with number of products

You can use your own css and javascript to design the html generated.