Customer registration: before or after making a purchase?

There aren’t many phrases out of the dotcom era that have survived in my vocabulary, but one that I think perfectly describes this situation is frictionless commerce. The idea is that the less effort, the less work your customers have to do between deciding they want to buy something and the transaction being completed, the better.
That’s why Amazon’s “One Click” was worth patenting for the company: it’s the ideal of making it as incredibly simple as possible for someone to go from wanting something to having purchased it. Heck, there’s not even an intermediate step where you confirm you really do want to buy the product!
The opposite of that is when you make it difficult for people to purchase products or complete their transaction on your site by putting up barriers including requiring them to register for an account or create a user profile before finishing their transaction.
This design mistake is so common, however, that there’s not just a name for the inevitable consequence of this approach to ecommerce — abandoned shopping carts. — but a small business space of companies trying to analyze why it happens and how to contact customers to have them complete the transaction. The answer is easy, of course: just make it as incredibly simple as possible to complete their transaction.
So it’s after they’ve completed their transaction that you want to ask them to register for the site, add a profile, save their purchase data, whatever, not before or during. Don’t add any “friction” to the transaction and your sales figures will inevitably increase.
Hope that helps settle your argument!