Magento mysql backup may fail to restore with following error if mysql backup was taken using simple "mysqldump" command.

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ERROR 1005 (HY000) at line 4367: Can't create table 'db_name.core_session' (errno: 121)

ERROR 1005 (HY000) at line 4367: Can't create table 'db_name.core_store_group' (errno: 121)
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Solutions

1. Use a backup created using magento backup tool

2. Use the script http://files.bytehouse.co.uk/dump_magento_database.sh to create a mysql backup

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wget http://files.bytehouse.co.uk/dump_magento_database.sh

bash dump_magento_database.sh

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Just run script as "sh dump_magento_database.sh".
Script will ask for mysql user name, password, mysql hostname, database name
Once the details are provided, script will take backup

Credits

dump_magento_database.sh script  is a modified version of https://gist.github.com/steve-ross/9958274     

Thanks to https://gist.github.com/steve-ross