Authentication of the merchant to accept credit card payments. Payment information integrity is ensured by the use of digital signatures. Special purpose certificates. Nonrepudiation for dispute resolution. Internet banking is definitely in its infancy but as time goes on, we should begin to see more and more banks provide online services to their customers.
Online banking saves cost for financial institutions and that is a good thing.
But where there is good, there is also bad. One bad thing is that online banking is not very safe. Banks are also faced with losing customers and revenue through alternative providers. Over the years, we have built up a lot of trust. There's a secure feeling that comes from dealing with a bank vs. a non-financial institution, and no killer payment application can duplicate that.