MySQL is the most popular but that doesn't necessarily mean it is the best. All database engines have their advantages and disadvantages so you should choose depending on an application you are developing. That said, I agree that for most ordinary websites MySQL is probably the best choice.
MySQL seems to be a good option if you want to associate it with PHP. It would be the best solution as MySQL is a well know product, easy to use.
PHP works great with MS SQL and Oracle also. However, it is strongly recommended to use MYSQL. It has been a tradition to use PHP-MYSQL and .NET-MSSQL
Posgresql and MySQL are the best. I have been using MySQL since I started to learn PHP and needed a database server. It's free and highly reliable when it comes to NOT crashing/"auto-deleting" everything. It's also easy to manage if you use for example phpMyAdmin.
Most public hosting companies provide a mysql database and provide support for PHP. If you using php in a coparate environment you may be forced to use oracle or SQl sever. I do concur with the other posters that the mysql/php is the most popular combination. And the best one, the best one for the job and depends on the size of the app, concurrent users, and few other factors.