I dont think there are any apps that use this atm but there are tons of potential uses where the alternative was getting people to give you their paypal api keys. Not the most secure thing but usually one of the only options if you were building something where the revenue has to go directly to a users account.

https://www.pay-pad.com/, http://shopify.com/ and http://shoplocket.com/ are a few off the top of my head.

In addition to Pay Pad, we also have Alerts for Stripe: http://www.pay-pad.com/alerts

Also, Zapier open-sourced a nice dashboard that uses Stripe Apps: https://board.zapier.com/

http://digmydata.com added Stripe support, too.