Drupal - How to let users register with their Facebook accounts?

Drupal for FaceBook is the one you need.

You can configure application settings and which information you want to get from users, such as email address.

Unlike other suggestions, this module does not rely on third party providers and registrations other than Facebook.

I've tried out all of the current suggestions, have used both Drupal for Facebook and FBConnect on sites in non-trivial ways, and only pain lies down those roads.

If all you need is authentication and maybe a few imported user profile fields (such as e-mail) go with FBOauth. Its newer, but is far easier to set up and use, and far easier to build off of if you're not trying anything too extraordinary.

The relationship between regular users and Facebook users depends a lot on the module you pick. In general all the modules create a table that associates FB ids with drupal user ids. How that happens varies widely. If you need a lot of flexibility in terms of account linking FBConnect is pretty full featured in that area but tends to be buggy elsewhere.

Facebook Connect works out of the box. I have been using it in a couple of sites.