In Drupal Commerce how do you auto login an anonymous user that has completed checkout?
In short summary to the link Clive posted in case if it ever gets deleted on the interwebs:

http://s1l.org/automatic-user-login-anonymous-checkout

Step 1 - Make sure Anonymous checkout is checked on. (Permissions > Access Checkout)

Step 2 - Make sure Commerce Immediate Login module is enabled: http://drupal.org/sandbox/simongeorges/1676742

Step 3 - Add a User Login Action to the default Commerce "Create new account for anonymous order" Rule (Configuration -> Workflow ->Rules)

--- rules/reaction/manage/Create a new account for an anonymous order

Step 4 - Click Add action > Login User (under system) > type "account-created" > SAVE

Step 5 - TEST!