In a country still very much in favor of paying more, such as Germany, its central bank, the Bundesbank, has been very worried about the arrival of bitcoins as well as other virtual currencies.

In general, banks see decentralized cryptocurrencies as a potential competitor to their role in the traditional fiat-currency-centric economy. If you didn't need an intermediary (the banks) to transfer money securely from one party to the other, a large part of the reason for their continued existence would disappear.

This is not to say that banks are always vehemently pro-fiat, a lot of banks are working on their own blockchain-based systems that they are still in charge of.

One of the most obvious examples (although not bank-owned) is Ripple (https://en.wikipedia.org/wiki/Ripple_(payment_protocol)), even if they have published their source code (https://github.com/ripple/rippled) they have been criticized for using a pre-mined scheme for their cryptocurrency (XRP), leading to a closed currency system that can be hard to enter for new players. From a security point of view, they also use far less validators than other similar networks, although thay are taking steps to remedy this situation.

The Ripple network is primarily used by large banks and bank consortiums and is poised, in my opinion, to be the "ready to buy" solutions for banks that feel threatened by cryptocurrencies and blockchain-based money transfer solutions.