PostgreSQL is MySQL's little brother in the open source world in terms of popularity, but very comparable (if not better) in performance.
PostgreSql hosting is also most common on Linux/Unix servers and often offered along with MySQL as an option. Can easily be used with programming languages such as Python, PHP and Java. It shouldn't add any significant costs to your web hosting account, but availability is a bit limited compared to MySQL and you won't find as many scripts available that utilise it.
