Table size for all databases:

SELECT TABLE_SCHEMA AS `Database`,
TABLE_NAME AS `Table`,
ROUND((DATA_LENGTH + INDEX_LENGTH) / 1024 / 1024) AS `Size (MB)`
FROM information_schema.TABLES
ORDER BY (DATA_LENGTH + INDEX_LENGTH) DESC;

Table sizes for a single database:

SELECT TABLE_NAME AS `Table`,
ROUND(((DATA_LENGTH + INDEX_LENGTH) / 1024 / 1024), 2) AS `Size (MB)` 
FROM information_schema.TABLES 
WHERE table_schema = "<database name>" 
ORDER BY (data_length + index_length) DESC;

Size of a single database:

SELECT TABLE_SCHEMA AS `Database`, 
ROUND(SUM(DATA_LENGTH + INDEX_LENGTH) / 1024 / 1024, 2) AS `Size (MB)` 
FROM information_schema.TABLES
WHERE TABLE_SCHEMA="<database name>";