At least for Oracle I run this query or ask the DBA to run it and send me the results. Results can be copied directly to a text file to be interpreted by Graphviz's tools, resulting in a database diagram.
SELECT '"' || Source.TABLE_NAME || '" -> "'
|| Destiny.TABLE_NAME || '";' AS For_GraphViz
FROM dba_constraints Source
JOIN dba_constraints Destiny
ON Source.owner='my_db_owner' AND Destiny.owner='my_db_owner'
AND Source.CONSTRAINT_TYPE='R'
-- theoretically this validation should be redundant
-- AND Destiny.Constraint_type = 'P'
AND Source.R_CONSTRAINT_NAME = Destiny.CONSTRAINT_NAME
ORDER BY Source.TABLE_NAME, Source.CONSTRAINT_TYPE, Source.CONSTRAINT_NAME
, Source.R_CONSTRAINT_NAME, Source.INDEX_NAME;
A similar query can be created easily for SQL Server, don't know about MySQL, PostgreSQL et al.