Drupal 7 provides you a lot of great options to customize the user registration form. The first place to look is under the configuration menu in the administration menu. Select "People" and then "Account Settings". Select the "Manage Fields" tab. Here you will see all the fields available to your users. You can add and remove fields here. To determine whether or not a field displays on the registration form, you need to simply edit it and un-check the "Display on user Registration Form" checkbox. Once you save, the field will no longer be available for users on the registration form. Most fields can be edited this way.
Some fields are added to the form on just the "Account Settings" page. Generally, if you scroll to the bottom of the page you may find some fields there to enable or disable. The location module, for example, is changed on this page. Generally you'll want to look for a checkbox that involves registration. For the Location module it's called "Collect during registration".
Finally, one thing you may want to do is remove the username field. This is a core part of Drupal, so a module will be required. We liked to use Email Registration. Simply enable this module. You will need to edit the welcome e-mail (Configuration -> People -> Account Settings) and replace instances of the token [user:name] with [user:mail]. You should change the token on all of the welcome emails, the account activation email, and the password recovery email at the very least.
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