haXe offers you two connectors in its standard library. Those two connectors can be used when targeting the PHP or Neko platforms.
Unfortunately, at the time of writing, the standard library does not provide any way to connect to databases when targeting C++.
So, on PHP and Neko, you will be able to connect to MySQL and SQLite databases. Note that these two databases systems work by following two different schemes:
MySQL is based on a client/server model where your application is the client and connects to the server using a login and a password.
SQLite databases are stored in a file on your filesystem. Therefore, you will have to make sure that your user has the correct access rights on the file storing your database. SQLite databases are really good when you don't want to depend on installing and running a server. This is particularly interesting when you want to create some locally running applications.