SHOW {DATABASES | SCHEMAS}
[LIKE 'pattern' | WHERE expr]
SHOW DATABASES lists the
databases on the MySQL server host.
SHOW
SCHEMAS is a synonym for SHOW
DATABASES. The LIKE
clause, if present, indicates which database names to match. The
WHERE clause can be given to select rows
using more general conditions, as discussed in
Section 19.28, “Extensions to SHOW Statements”.
You see only those databases for which you have some kind of
privilege, unless you 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.
MySQL implements databases as directories in the data directory, so this statement simply lists directories in that location. However, the output may include names of directories that do not correspond to actual databases.

User Comments
Hopefully useful to have documented here - if you need to dynamically determine the active database, SELECT DATABASE(); will return one row containing the current database name for the active connection.
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