mysql-list-database-sizes

SELECT table_schema AS "Database name", SUM(data_length + index_length) / 1024 / 1024 AS "Size (MB)" FROM information_schema.TABLES GROUP BY table_schema;

If you want to just list out the number of databases

SELECT count(*) FROM information_schema.SCHEMATA WHERE schema_name NOT IN ('mysql','information_schema');

gets you a count of all databases in the instance