It depends what country you live in. In the United Kingdom, all the major banks offer good online access to their accounts. These include Barclays, NatWest, Santander, Lloyds, and Halifax. I believe that internet only accounts are available through NatWest, Barclays, Nationwide, Santander, HSBC, and RBS offer internet only accounts. You may find this website helpful for comparing the various services of internet accessible and internet only banking accounts in the UK: www.money.co.uk
