A bank called Skandiabanken in Norway now supports Bitcoin. However you cannot purchase the Bitcoins through the bank, you'll be redirected to Coinbase in order to buy.

I don't have this bank myself, so I cannot test this. It seems like it's just linked to Coinbase and the bank does not store the coins on their servers.

This feature is in a beta phase, and the laws in Norway could cause conflicts. I think this is a huge step, and I hope this will soon be supported in more banks. This feature is mainly for investors, you cannot use it to pay bills and such.

Here's a link to the article translated to English:  https://translate.googleusercontent.com/translate_c?depth=1&nv=1&rurl=translate.google.no&sp=nmt4&tl=en&u=http://e24.no/privat/bitcoin/naa-faar-du-bitcoin-i-nettbanken-kan-ikke-fornekte-ny-teknologi/23996559&usg=ALkJrhjVd47hlRvCuPcMw4r7-8SKmywfYw