Hi,
If you want to use remote database systems like PostgreSQL or MySQL, you'll have to do some work first because neither of these provide native Android build of their package.
For PostgreSQL, there's a wiki article here.
For MySQL, there's a wiki article here.
As @jsulm already noted, it's usually a bad idea to design an application which access a database directly through an open network so take care to secure the connections appropriately using encryption.