Is there a Bitcoin bank, which gives interest on my deposit? Is there any Bitcoin bank I can place my Bitcoins in that will give me a decent interest rate. It should be at least 1% for it to be worth it.
Please Take Note: Flexcoin has been hacked and is no longer operating.

Original Post shown below:



Right now, the closest thing you can find to a bank is Flexcoin. If you keep your money there, you will receive a variable interest (they call it discount for legal matters) every month. They also have a user defined cold storage service available for those who want to keep their funds offline.

Here is how it works. Every time you withdraw money from Flexcoin, you pay a fee:


  Fees:   
  
  Flexcoin to Flexcoin = FREE
  Bitcoin to Flexcoin = FREE
  Flexcoin to Bitcoin = 0.01 BTC or one half of one percent of the transaction amount (whichever is greater)
  Cold Storage Transaction Fee (outbound) = 0.02 BTC or one percent of the transaction amount (whichever is greater)
  Cold Storage Transaction Fee (inbound) = 0.01 BTC or one half of one percent of the transaction amount (whichever is greater)


This fee is used to pay miner fees and keep the service running. The rest of it is distributed among clients:


  Discount Payout:
  
  70% of the fees collected are disbursed to the account holders as
  discount payments on any fees already paid or any potential future
  fees, based on the following formula…
  
  (your account balance / total balance of all flexcoin accounts) *
  ((all fees collected – miner fees) * 0.7)


Here are two bitcointalk threads about the discount payments for the first two months.

As a final note, I would like to say that I personally think that this kind of service is not very useful right now because the Bitcoin price is too unstable. For example, yesterday the price dropped 15%. Any interest you might earn becomes irrelevant in this scenario.