Apache has a very decent authentication scheme. In Apache you define what are called "Authorization Realms". You can define these in your apache configuration files on a directory or site, or you can define them in a .htaccess file. Each of the Authorization Realm specifications will point to a password file and will look like this:

This file defines a few things, it defines which users to allow, where the passwords are stored, and the name of the Authorization Realm. The name of the authorization realm is important, because you can have multiple layers of authentication. For example, you could have a folder that any valid user can access, and a subfolder which only 2 specified valid users have access to. If you ensure that the AuthName is set the same, the user will only have to enter their username and password once, whereas if you have different AuthNames, the user will be required to pass into each realm separately, even if the password file is the same.

Important Security Note

Any time you use Authorization through Apache, you should ensure that your users are connecting with HTTPS, otherwise the passwords will be sent in plain text, and anyone listening in the middle could see and capture them.