In Drupal 7, is there a way to add more fields to the registration process? I was thinking along the lines of birthday, fullname, gender, twitter, etc. Also how do I access this data once it's in, so I can output it to my template files?
Since D7, field management is included in the core. Almost every kind of content has now the ability to be managed with fields.
You can go to admin/config/people/accounts/fields to manage user fields. There is also a tab for managing the display.
Administration » Configuration » People » Account settings » Manage fields
Make sure once again by edit the new fields and its check box for Required field and Display on user registration form will be enabled.