How can I include a list of what a user ordered (the line items) in an e-mail sent by Drupal Commerce?
The [commerce-order:commerce_line_items] token does not work when Completing the checkout process, which is the event for which the Send an order notification e-mail rule is triggered.

Instead, one way to do this is to use the Commerce E-mail module, which provides a [commerce-order:commerce-email-order-items] token and a new interface for editing the e-mail.  Note that you will need to disable the e-mail-sending rule when using this module (or else you will get duplicate e-mails, as the module help points out).