You need to decide how you want to save your data. You can save the data in an XML file, a plain text file, or anything else.
The reason you're seeing so many examples of people using SQL is because relational databases have already solved a lot of the issues you're likely to run into when storing and retrieving data. That means in most cases, it's much easier to use an SQL database (even a lightweight embedded one) than to try to come up with your own library for retrieving and saving data.
A note about saving passwords
Bear in mind that any data you save on a client's computer is going to be accessible to that client. You can use tricks to make it very difficult for someone to get to that data, but there's nothing your program can do that a clever hacker won't be able to mimic. The only way to avoid letting users see the stored passwords would be to make the user provide a "master" password that gets converted into a key that is used to encrypt the other passwords. This way, only users that know this master password would still be able to get the stored data.
Storing data in a relational database is not sufficient to prevent users from accessing that data.