If you're looking for an actual bank, BankSimple is going for this. The founders are smart ex-finance dudes, and Alex Payne is the guy in charge of the web app.
I had a conversation with the best banker I know about BankSimple. This is a guy that founded a bank in a major US city that had absolutely -0- non-performing loans, through the crisis. That is amazing when you compare it to the rest of the banks in our nation. The only one that come close in terms of performance/size is First Long Island. Here's what the banker said about these online bank start ups:
"One of the main problems with "online" banks is how do they make money. Most if not all have loan volume from somewhere else and are trying to find deposits to fund it - ING is an example. They try the internet route instead of opening expensive branches. ING has kind of dropped off the radar lately because they have credit problems (and I think it is a Dutch bank and you have
read about the European problems).
If these people want to start an internet bank with no fees and make it up on the NIM, they need to invent a way to get people to borrow on the internet. No one has been able to do that yet with the exception of some payday lenders. Also,
most of the internet banks so far have competed on price. They offer higher rates - which tend to attract "rate-shoppers". If they are not the highest rate, the rate-shopper will go wherever the highest rates are."
For a start up, I'm not sure if they will be able to compete on price. Banks like Wells Fargo benefit from their economies of scale because they are able to gather cheap deposits by cross-selling products (which is attributed to their success).
I'm anxiously awaiting for them to come out of private beta. I've been following them for a little while now. It's exactly the kind of thing I hope to see more of..