It's common for spouses to share a bank account, and most probably don't want to think about what might happen to the money if one of them dies. In most cases, however, nothing changes. The bank typically won't freeze the account – at least not the entire account – and the surviving spouse can go on making deposits and taking withdrawals just as before.
Access to Funds
When spouses hold a bank account jointly, they do it in one of two ways. The names on your account either read "John Doe and Jane Doe" or "John Doe or Jane Doe." If the former is the case, you must sign checks together and sign together for withdrawals. This automatically means that although your bank won't necessarily freeze the account or hold the funds when one of you dies, you don't have access to the money either, at least not until the probate court sorts through the matter. If the latter is the case, either of you can take out money during your lifetimes without the consent or cooperation of the other. Therefore, your spouse's death would have no impact.
Death of One Owner
Joint accounts typically carry rights of survivorship because of their very nature, but check with your bank to make sure this is the case with yours. Normally, if either of you can access the account without the other during your lifetimes, this continues after one spouse dies, and the bank can't intercede with or overrule this right. The nature of the account doesn't change because one of you has died, and the bank has no right to hold the account funds. At death, ownership of the entire account vests automatically with the survivor. You would generally only have to provide the institution with a copy of the death certificate to have your deceased spouse's name removed from the account.
An exception sometimes exists if a deceased spouse was collecting Social Security benefits. Most funeral homes notify the Social Security Administration of a death when it occurs, and Social Security will cease payments. If a check has already gone out in the mail, however, the surviving spouse or the executor of the estate must return it to the SSA when it's received. If the payment is directly deposited into the decedent's account, the bank might hold or freeze this portion of the balance, because the bank is responsible for returning it. It legally belongs to the government after the recipient has died. In no event should you withdraw this money even if the bank doesn't freeze it and even though you still have full access to the account – it's not yours.
The funds in a joint bank account are not subject to probate, and the deceased spouse cannot assign them to someone else in his will. The other account owner has a legal right to access the funds, and the law can't step in and take this away any more than the bank can. The only exception is if you and your spouse have a written agreement that half the account should go to the estate and be distributed to other beneficiaries.