Opening a checking account online is a tough challenge for financial institutions, even more than other equivalent value financial products. Why? Using a dating analogy, at the 'open checking account' point in a customer / bank relationship there is a lot of desire, but little trust.
A checking account is often the first step in commitment that a customer and bank make together. So without physical proof of the customer's identity and background it is extremely difficult for the bank to know if the customer is a 'good person' or a 'bunny-boiler'.
I ran across an article on GonzoBanker from about 5 weeks back by Terence Roche, which introduces the approaches that some banks and software vendors are taking to tackle the issues around online account opening.
In Terence's mind, if you are a bank that wants provide checking account online applications you have to be a little crazy. Obviously Terence isn't one for online blind-dates of the match.com kind! I have to agree with him though. It is far easier for companies to start out offering online applications for other products, such as savings accounts, CDs and brokerage. Since these can be set up to only feed from the checking account there are few of the identity, fraud and AML issues associated with a completely unknown person.
As with many financial products, know your customer and their identity is one of the hardest components to achieve online. Into the future this is likely to require banks to share customer indentity information, although this not only presents technical (interoperability) issues, but also privacy issues as well.
Blind dates are difficult. In the banking world its far better to be referred by a friend to avoid relationships with stalkers and freeloaders.