Banks are only necessary if people need to deposit their money in them. With bitcoin there is really no reason to keep your bitcoins in a bank.
However, it is foreseeable that people may want to keep their bitcoins safe by keeping them in a bank that they trust. Even if this occurs, bitcoin allows for PROOF OF SOLVENCY which means that everyone can verify that the bank is actually storing their bitcoins for them.
This effectively eliminates the possibility of Fractional Reserve Banking. Who in their right mind is going to give their bitcoins to a bank that turns our around and lends them to other people and makes bets in the stock market with them? Nobody.
Only those banks that embrace PROOF OF SOLVENCY will survive with bitcoin. Those banks that try to hide what they are doing with people's money or try to give some reason why people should allow them to keep only 3% of deposits in reserve and lend the rest out, will not survive. Nobody will use these when there are PROVEN SOLVENT banks now in existence.
What you think?
In an ideal world
(a world where banks aren't this powerful and people are willing to take responsability) banks will become obsolete for the citizenship and small bussinesses, only useful for companies in need of big amounts of liquid assets. The reason behind this statement is that not very long ago most of the tasks that banks do today were solved in contracts among individuals.
For example the payment conditions for mortgages were stipulated in a contract between the interested parties (usually an individual owner and the buyer) and was in rare ocassions where a bank was involved. The contract was as valid as any other legal document and the law protected the owner in case of dues being unpaid or the buyer in case any of the contract conditions weren't met by the owner. Another example are personal loans which were done among individuals as well and all the conditions and interest rate arranged via a notary contract. Nowadays this would be a very valid way for people and small bussiness with some saving to have a good return for an investment with small risks since, again law protected the loaners against unpayment and loanees against not stipulated in the contract.
Right now I don't recollect the link but there are law firm websites which promotes and try to educate the population about the laws that were valid in the past can still be applied today for doing these kinds of bussiness arragements without a bank being part of the equation. A bank gives more security to the transactions and makes all the work for you but if the parties take the time to prepare the contract and hire a notary and educate themselves a bit about contract law both will benefit more since they won't have a middleman who asks for its share.