Near as I can tell you're allowed to have users punch their credit card into your app and bill them using your own gateway, on both iOS and Android. But the recent events with Sony make me unsure. And Google seems like they'd be more liberal about in-app payments, but these docs say they are for "virtual" goods.
There's also the Amazon mobile app, the B&N Bookstore app, the NewEgg Mobile app, even Sears2go.
From the current docs for Google in app purchase: http://developer.android.com/guide/market/billing/billing_ov... "You can use in-app billing to sell only digital content. You cannot use in-app billing to sell physical goods, personal services, or anything that requires physical delivery."
I'd check the terms and conditions of the stores about using other payment gateways as well
http://www.android.com/us/developer-distribution-agreement.h...
Payment Processor(s): Any party authorized by Google to provide payment processing services that enable Developers with optional Payment Accounts to charge Device users for Products distributed via the Market.
However the advantage of the Android platform is that the market is not the only app store available and also app stores are not the only means of distribution
From the iPhone App Store Guidelines
11.2 Apps utilizing a system other than the In App Purchase API (IAP) to purchase content, functionality, or services in an app will be rejected
11.3 Apps using IAP to purchase physical goods or goods and services used outside of the application will be rejected
20.4 Apps that allow a user to directly purchase a lottery or raffle ticket in the app will be rejected
21.2 The collection of donations must be done via a web site in Safari or an SMS
http://stadium.weblogsinc.com/engadget/files/app-store-guide...
Per 11.3, you cannot use Apple's IAP system to sell physical goods. You can use your own.