To those who say "I almost went with PayMill, thank god Stripe is here now" don't forget that PayMill features direct debit. Depending on who your customers are this might be an important feature for you!
For most SaaS/e-product models "direct debit" is not an option because a customer can do a refund without a reason for at least 6 weeks. It also has no CVV2, so you can just abuse some charity bank details for a direct debit purchase. Good luck dealing with fraud.