PostgreSQL is a Sophisticated open-source Object-Relational DBMS supporting almost all SQL constructs, including subselects, transactions, and user-defined types.
pg_dump is an effective tool to backup postgres database. It creates a *.sql file with CREATE TABLE, ALTER TABLE, and COPY SQL statements of source database. To restore these dumps psql command is enough.
Similar to mySQL, postgreSQL is very famous and feature packed free and open source database.