Drupal - User Registration Module for Drupal

There are a couple of options for this.

To get profile fields the most common solution is the profile module included in Drupal core. Go to Administer > Site building > Modules and enable it under core-optional. Then you can configure the Profile module at Administer > User settings > Profile and in the settings you can say whether the fields will show during registration or not.

To get a captcha during registration you will need one of a couple of modules:

I prefer HCaptcha because it works very well and even can earn you some money, but it sends your content to an external site to do some verification.

There is also Captcha which provides integration with other options.

The typical choice for this is to use a combination of content_profile to create the user profile as a node, content_profile_registration, a component of content_profile, to create such a profile at registration using such a full-fledged node edit form, and possibly auto_assign_role if you have multiple types of users with distinct profile types.

For the captcha part, Mollom is an interesting service, as Greggles suggested, but you might also want to consider reCaptcha, which is good too at even doubles as a public service.

It would appear that the recommended process now is creating fields. From the Drupal site:

The Profile module is deprecated in Drupal 7. It is kept around only to provide an upgrade path for Drupal 6 sites that used it. Use of the Profile2 module or creating fields directly on the user entity is recommended in Drupal 7.