Today I got this mysterious error message after moving a Magento website to a new server.
Magento Notice: Undefined index: 0 in .../htdocs/app/code/core/Mage/Core/Model/Mysql4/Config.php on line 92
Turns out this was due to a faulty import of the database. Apparently there are a few tables where using an id of 0 in the auto_increment column has a particular meaning and is intended. When restoring the MySQL dump through Navicat it replaced id values of 0 in auto_increment columns with new auto-incremented ids instead of 0 which broke Magento.
To fix this I simply dropped the whole database and reimported the dump using the official MySQL command line client (mysql -u username -p db_name < scrip.sql) and everything worked fine.