SET GLOBAL sql_mode = '...,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,NO_ZERO_DATE';
SET SESSION sql_mode = '...,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,NO_ZERO_DATE';

mysql> show VARIABLES LIKE 'sql_mode';

+---------------+-------------------------------------------------------------------------------------------------------------------------------------------+
| Variable_name | Value                                                                                                                                     |
+---------------+-------------------------------------------------------------------------------------------------------------------------------------------+
| sql_mode      | ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,NO_ZERO_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION |
+---------------+-------------------------------------------------------------------------------------------------------------------------------------------+
mysql> SELECT @@GLOBAL.sql_mode global, @@SESSION.sql_mode sessionG
*************************** 1. row ***************************
 global: ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,NO_ZERO_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION
session: ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,NO_ZERO_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION
1 row in set (0.00 sec)


mysql> create table fechas(fecha DATE NOT NULL);
mysql> insert into fechas values(0);
ERROR 1292 (22007): Incorrect date value: '0' for column 'fecha' at row 1
mysql> insert into fechas values('0000-00-00');
ERROR 1292 (22007): Incorrect date value: '0000-00-00' for column 'fecha' at row 1