In the module installer file, create the attribute like this, and it will appear in the customer backend.
An extra part is needed for newer version of Magento (not sure from when exactly, but it is true as of Magento Community Edition 1.6 and up).
The "used_in_forms" key cannot be in the array passed to the addAttribute call directly (won't work). It probably contain the names of the forms from which the customer model will accept the values and not ignore them when being saved.
Known values are at this question's answers: Can no longer add registration fields in Magento 1.4.2.0 (The answer by Folker Schellenberg)
I think it is the name of the controller and action that rendered the form. This name is also the main layout handle name of the page (eg: customer_account_edit).
It should be noted that the customer form in the front-end is HTML-based. It doesn't dynamically render inputs from the attributes like the backend forms. This means that if these attributes should be input by the user, the template needs to be amended to contain the proper input tags as well (and the proper value added in the used_in_forms array).
$attributeCode = "uploaded_file";
$attributeLabel = "Uploaded file";
$installer->addAttribute('customer', $attributeCode, array(
'type' => 'text',
'input' => 'file',
'label' => $attributeLabel,
'global' => true,
'visible' => true,
'required' => false,
'user_defined' => false
));
// For newer versions of Magento, otherwise won't show up.
$eavConfig = Mage::getSingleton('eav/config');
$attribute = $eavConfig->getAttribute('customer', $attributeCode);
$attribute->setData('used_in_forms', array('customer_account_create', 'adminhtml_customer'));
$attribute->setData('sort_order', 200);
$attribute->save();
Another possible type is 'image' which renders exactly as 'file' except it shows the image in a preview box (a small one). Maybe good for customer photo ?
Also, noteworthy is that is this specific for the customer form (the class that handles this type of attribute is: Mage_Adminhtml_Block_Customer_Form_Element_File and Mage_Adminhtml_Block_Customer_Form_Element_Image), so this won't work in a product attribute without custom work.
Hope this helps !