This is a very good one and will most likely become one of the heated discussion about BTC. The reason being is that, BTC utterly destroys the money making scheme of banks. Banks primarily earn money by allowing the people to deposit their money in a very stagnant (with very very little interest rate on it) financial vehicle. The banks then of course use this money to lend to people, and circulate the money but still keep a good amount of money for the depositors to withdraw their money at any point in time. Imagine if people can easily store their money in an e-wallet or just dispose majority of their fiat money and turn it to bitcoin for transactions. There'd be no point in keeping your money in the bank. If the Bitcoin will become as stable as the fiat money, trading and exchanging of currency will be of very little cost. You can make an exchange to the other side of the world instantaneously, you can store your purchasing power in it with very little risk of being affected by the inflation.
This only my opinion but in the near future, if BTC will be accepted and adopted by our government, the banks still be playing a very important role but they will take a MASSIVE hit as a lot of people will be transferring their money in bank to get a portion of the digital currency.