Not necessarily, it can actually help if you pay them in full each month. Watch out because if you have too many cards and miss or make minimum payments, disaster may be around the corner.
From Learn Vest
3. Will having too many cards hurt my credit?
It’s not the number of credit cards that you have, but how you use them. You could have lots of credit cards and still have great credit—or you could just have one or two and maintain a great credit score. (Check out this infographic that shows how folks with higher credit scores actually have a higher number of credit cards.) Just remember that the more credit cards you have, the more risk you take on of missing a payment. Your credit will benefit as long as you keep up with your monthly payments, but you still need to be careful not to charge items that you can’t pay off each month–that’s an easy road to credit card debt.