Magento - Accessing a customer's wishlist

You're very close to your target.

$wishList = Mage::getSingleton('wishlist/wishlist')->loadByCustomer($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.

Your code is correct. There may be customer is not loaded. here is code.

$customer = Mage::getSingleton('customer/session')->getCustomer();
$wishlist = Mage::getModel('wishlist/wishlist')->loadByCustomer($customer, true);
$wishListItemCollection = $wishlist->getItemCollection();

foreach ($wishListItemCollection as $item)
{
   // do things
}

In any template, using magento 1.8, this works

Total: <?php echo $this->helper('wishlist')->getItemCount() ?>

// Items
$this->helper('wishlist')->getWishlist()->getItemCollection();