My ecommerce site has a variety of pages specific to the checkout-out process. These include "Cart", "Billing", "Shipping", "Discount", "Finish", and "Complete Order". In general, should I be including these in my sitemap.xml?
Those pages are usually not available to search engines because they require a user to actively add items to a cart and then provide information to continue along the purchasing process. Search engines will not complete that process and as a result should never be able to reach those pages. If your site is built well, anyone with an empty cart should never be able to see those pages and should be taken to an empty cart page instead.
So I would say, no, don't add them to your XML sitemap since they aren't available to search engines to crawl and index nor for new visitors to access.