There is the option of GoCardless (https://gocardless.com/) in the UK, however they use the Direct Debit system rather than card processing which does somewhat limit you geographically.

Aren't they really the "Anti-Stripe" more akin to Dwolla? Banish Credit Cards altogether? Also, I heard there were changes in European direct deposit/ACH laws (the approach Gocardless takes) that will allow them to be European, not just UK, very soon.