When using the Joomla! Update component to update from 2.5.19 to 3.2.3, the update failed with the following error:
Fatal error: Call to a member function isAdmin() on a non-object in /path/to/joomla/plugins/system/remember/remember.php on line 42
From that point, I had to restore from a backup (thank you Akeeba).
If you encounter this error, before updating, disable the System – Remember Me plugin.