Magento – Accessing a customer’s wishlist

$wishList = Mage::getSingleton('wishlist/wishlist')->loadByCustomer($customer);
$wishListItemCollection = $wishList->getItemCollection();

if (count($wishListItemCollection)) {
    $arrProductIds = array();

    foreach ($wishListItemCollection as $item) {
        /* @var $product Mage_Catalog_Model_Product */
        $product = $item->getProduct();
        $arrProductIds[] = $product->getId();
    }
}

The array variable $arrProductIds will now contain the list of all Product IDs that have been wishlisted by that specific Customer.