Oh okay. That's normal, depending on the app. Just choose to not allow it unless it is something you want to be alerted on such as weather updates, news updates and stuff of that nature. If you choose to not allow it and then find that you would like to receive push notifications from the app or apps, you can easily enable it in the settings menu.
I understand, but no one can make that determination for you. It's your phone and your decision to make. Having said that, with the exception of email, I have push notifications set up for weather alerts, sports scores for certain games via the ESPN app, Twitter DMs and a few other apps.