Clearing or Updating Cart Issues Following Magento 1.9 Upgrade

Please add the following line under the <form> tag.
File path - app/design/frontend/default/[you theme name]/template/checkout/cart.phtml file

<input type="hidden" name="form_key" value="<?php echo Mage::getSingleton('core/session')->getFormKey(); ?>" />

if there is login issues then please add the following code in the login page which is under persistent folder.

<input type="hidden" name="form_key" value="<?php echo Mage::getSingleton('core/session')->getFormKey(); ?>" />