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.