Just so nobody gets the wrong idea, 0% APR doesn't mean there aren't any restrictions. You'll still have to make your payments on time, and chances are if you don't, your 0% interest deal will evaporate. In the case of a credit card, you can't charge up to the limit and assume you don't have to pay anything back until the 0% promotional period expires. Be very careful about late payments also - the fine print may say that if you are late, your interest rate goes up to 22% or some horrendous number.
In the case of a car, as vi_edit said, it's usually a trade-off between the 0% interest and a rebate. You'll have to figure out which is the best way to go. To keep your options as flexible as possible, tell the dealer you will be paying cash and you're only interested in the best price. Once you negotiate a price, you can change your mind and give back the rebate to take the 0% interest if that's what is best for you. But waiting until the end gives you the bargaining power and you know exactly how much the rebate is, so they can't play games.