Número de registros totales de la base de datos
select sum(table_rows) from information_schema.tables where table_schema = 'DATABASE_NAME';
Número de registros por tabla de la base de datos
Select table_name, format(table_rows,2) from information_schema.tables where table_schema = 'DATABASE_NAME' Order by table_rows desc;
Tamaño en megas de cada tabla
select table_name, round((data_length+index_length) / 1024 / 1024) as `Size (MB)`
from information_schema.tables where table_schema = 'DATABASE_NAME' Order by (data_length+index_length) desc;
Y esto es todo, feliz programming
Saludos
Alex.