Making intra-bank transactions more efficient is one; the floor of money transfers will be both cheaper and faster. Wire transfers are expensive and can be very slow (sometimes more than a day) for example. Bitcoin being a real transaction mechanism between institutions that is cheaper than wires and faster than wires (works on Sunday!) puts pressure on the banks to either compete or adapt. Another example is enablement of micro-payments (perhaps on side-chains) where conventional money transfers don't scale well - someone, not your (artists) preferred broker, is holding your money until it aggregates up to a transferrable sum. Now there's pressure to make that sum smaller and the transfer frequency greater.

And, although not everyone needs this, for those of us that have been in the situation of doing international money transfers, they are a huge pain, unreasonably expensive, and slow too. Bitcoin puts pressure on all this, and I believe we're already seeing companies pop up that offer transfers in your preferred currency but are using Bitcoin behind the scenes to settle the transfers.