Many times that available line of credit on your new card is equal to the total you're purchasing, Bowne says.

So, in essence, "you're opening up a maxed-out credit card, which doesn't look good on your credit report," she says.

It can also damage your credit score.

Here's why: Your credit score calculates how much of your revolving credit lines you're actually using. For the optimum score, that figure should stay below 10 percent, says Barry Paperno, consumer affairs manager with myFICO.com.

To find out how a zero percent financing offer would affect your credit, determine whether you'd be opening an actual close-ended loan for a set period or a revolving account. Ask how this loan will report to the credit bureaus, says Frank. Will it show up as a credit card or revolving account, or as a close-ended loan?

When you get the answer, consider your own situation. If you're planning a major purchase in the next year, such as a home or car, it might be cheaper to skip opening a new account, pay cash and preserve your credit score.