Payment by Invoice
In response to the question why would you want to not use a payment gateway:
I have a client who wants only registered customers with accounts set up with them in the offline world to be able to order from their website. They want their customers, once registered with their website, to be able to place an order and then pay 'on invoice' as they already do. therefore just the website to store the order along with the registered shoppers id and then inform the merchant that an order has been placed. Personally I'm looking at this now and think it's probably a case of replacing the checkout buttons with 'place order' buttons and then writing a quick script to email the merchant who can then access the order details from their CMS. Would be much quicker and easier if there was a 'Payment on Account' or 'Invoice with Order' option as some other shopping cart systems do though.