I prefer the no contract plans, personally. As fast as phones and services are updated these days, and with all the good pre-paid plans out there now, it just seems silly to limit yourself to one provider for one or two years. That being said, we are currently on a contract plan because our new provider paid for our phones and paid our old contract in full, plus gave us a Visa gift card to switch. We couldn't pass that up.
Your credit score can be affected if you don't pay your bill on time with a contract plan. You probably won't be able to get a contract plan if you have bad credit when you apply.