You have a lot of responses about the prop being balanced, I want to make sure you understand that the PLANE needs to be balanced. I don't think anyone will disagree with that. As for props, you have seen where some say yes, some have never had problems. I want to make sure you understand that you should absolutely check the balance of your plane, (laterally as well as longitudinally) before every flight.

It should be slightly nose heavy (with tank empty) and should be level when checking balance from nose to tail (one wing should not be heavier than the other).