From a credit standpoint it's never a good idea to close out credit card lines because it reduces your available credit capacity thereby potentially dropping your credit score. On the other hand opening new credit card lines can also have a negative impact on your credit score as it thrusts you into a new credit scoring bracket. There are several different scoring brackets that exist within the credit scoring algorithms so it's impossible to know which one you fall into. However you should be aware that every time you add new credit to your profile you're shifting yourself into a new bracket and possibly weakening your credit score.
Enough technical talk, the questions that you need to ask yourself is 1) am I planning to pay off this debt anytime soon & 2) do I have a plan to pay this debt off when the 0% offer on this card expires. 0% credit card offers are ok if used responsibly, but when abused they can put you and your credit situation in a world of trouble. Double check the standard interest rate on the card that you are considering switching to, there's a good chance that it's very high (18%-27%) since they have to make up for giving you 0% interest for 6-10 months. Contact your existing credit card companies and ask them if they would consider extending you a 0% promo offer if you balance transfer to them. If approved this will put a new inquiry on your credit bureau, but it'll save you from having to open a new credit line.
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