By default user registration is allowed in Joomla 1.5. You will just have to enable the login form. To do this, follow the steps below:

Step 1. From the Joomla admin panel go to Extensions -> Module Manager:

Step 2. From the top right menu click on [New] and check the "Login" option:

Step 3. Click on "Next" from the top-right menu to proceed.

Step 4. From the options that appear we will make only one change:

Title: Login

Step 5. Save the progress by clicking on [Save] from the top menu and you will find a login form on your site.