$orders = Mage::getResourceModel('sales/order_collection')
                ->addFieldToSelect('*')
                ->addFieldToFilter('customer_id', Mage::getSingleton('customer/session')->getCustomer()->getId())
                ->addFieldToFilter('state', array('in' => Mage::getSingleton('sales/order_config')->getVisibleOnFrontStates()))
                ->setOrder('created_at', 'desc')
            ;



count($orders->getData()) returns 3; OK

count($orders) returns 2; NOK

or

$orders->getSize() returns 3 : OK

$orders->count() returns 2 : NOK

<?php
$customerCollection = Mage::getModel('customer/customer')->getCollection()
   ->addAttributeToSelect('entity_id');

foreach($customerCollection as $customer){
   $_orders = Mage::getModel('sales/order')->getCollection()
   ->addFieldToFilter('customer_id',$customer->getId());
   $_orderCnt = $_orders->count(); //orders count
   echo 'Customer with ID '.$customer_id.' has '.$_orderCnt.' orders';
}
?>

<?php
    $orders = Mage::getModel('sales/order')->getCollection()
    ->addAttributeToFilter('status', array('eq' =>  Mage_Sales_Model_Order::STATE_COMPLETE));
?>

$orders = Mage::getModel('sales/order')->getCollection()
    ->addAttributeToFilter('status', 'your_status');
$array = array_count_values($orders->getColumnValues('customer_id'));

foreach ($array as $customerId => $orderCount) {
    echo "Customer ID : " . $customerId . " Order Count : ". $orderCount. "<br>";
}

$orders->getColumnValues('customer_id')

$array = array_count_values(array_map(function($v) {
    return (is_null($v)) ? "?" : $v;
}, $orders->getColumnValues('customer_id')));