Joint bank accounts don't go through probate. If you co-own an account, say with your parent, spouse or business partner, her death gives you automatic full ownership of the account. Bypassing probate does not give you a free pass on taxes, however. When you inherit your co-owner's money, you may have to pay inheritance tax.
A joint bank account is co-owned by two or more people. Depending how the account is set up, the owners may have to make withdrawals and other decisions together, or each owner can withdraw individually. Power over the account has nothing to do with who contributed the money. If your parent puts your name on his account to help him manage his money, all the money becomes yours when he dies, even if you didn't put any money in.
As far as your state's tax collectors are concerned, you and your co-owners each own an equal share of the money. For example, if you and your mother have a $12,000 joint account, you have $6,000 each. When she dies, you inherit $6,000. If you're the one who put all the money in the account, that makes no difference. Legally, when she dies, you still have a $6,000 inheritance, even though it's your money.
As of 2013, only seven states charge inheritance tax: Indiana, Iowa, Kentucky, Maryland, Nebraska, New Jersey, Pennsylvania. If you live in one of those states, or the deceased co-owner did, your inheritance may be subject to the tax. The tax bite depends on your relationship with the deceased. Spouses don't pay any inheritance tax, and some states also waive the tax for sons and daughters. If the co-owner is a friend or business partner, you take the full hit.
If you're staring at an inheritance tax bill, it may comfort you to know that you don't do the paperwork. The deceased's executor handles taxes on the estate assets including inheritance tax. If, say, you and the deceased had a third owner on the account, that simplifies things: the executor only submits one return for both of your tax bills. If there's estate tax due on the account, the executor handles that too. (ref3)