MySQL
MySQL (pronounced either mai-es-kyu-el or mai-see-qwul) is a multi-threaded, multi-user, SQL Database Management System (DBMS). MySQL and PHP interact extremely well. If MySQL was the peanut butter, then PHP would be the jelly. MySQL, in combination with PHP, can be used to create dynamica websites, and most PHP scripts require a database, which is almost always MySQL.
MySQL has over six million installations, with sites such as Facebook, Digg, and Crucial using it as their database of choice.
Clients are free to create as many MySQL databases as they need, but please see the Terms of Service and Acceptable Use Policy regarding databases and server resources.