Magento products by categories

<?php
$_cat         = $this->getCurrentCategory();
$_parent      = $_cat->getParentCategory();
$_categories  = $_parent->getChildren();

/* @var $category Mage_Catalog_Model_Category */
$collection = Mage::getModel('catalog/category')->getCollection();
/* @var $collection Mage_Catalog_Model_Resource_Eav_Mysql4_Category_Collection */
$collection->addAttributeToSelect('url_key')
    ->addAttributeToSelect('name')
    ->addAttributeToSelect('is_anchor')
    ->addAttributeToFilter('is_active', 1)
    ->addIdFilter($_categories)
    ->setOrder('position', 'ASC')
    ->joinUrlRewrite()
    ->load();

$productCollection = Mage::getResourceModel('catalog/product_collection');
$layer             = Mage::getSingleton('catalog/layer');
$layer->prepareProductCollection($productCollection);
$productCollection->addCountToCategories($collection);
// $productCollection should be ready here ;-)
?>

$productCollection = Mage::getResourceModel('catalog/product_collection')
                             ->addCategoryFilter($category);

$categoryId = 123; // a category id that you can get from admin
$category = Mage::getModel('catalog/category')->load($categoryId);

$products = Mage::getModel('catalog/product')
    ->getCollection()
    ->addCategoryFilter($category)
    ->load();

print_r($products);