Syntax:
SHOW DATABASES [LIKE 'pattern']

SHOW DATABASES lists the databases on the MySQL server host. As of
MySQL 4.0.2, you see only those databases for which you have some kind
of privilege, if you do not have the global SHOW DATABASES privilege.
You can also get this list using the mysqlshow command.

If the server was started with the --skip-show-database option, you
cannot use this statement at all unless you have the SHOW DATABASES
privilege.
