A puppy trying to playfully bite is normal but yes you should try and stop the biting behavior and not let it get out of hand.
When your puppy starts to bite you or someone else use teething toys to redirect the puppies attention so they won't be inclined to bite you and will go after the teething and chew toy instead.
Use a taste deterrent on your body to stop the dog from biting you in those area and in some severe cases use a spray bottle to stop the puppy before it starts to bite you or someone else.
Your puppy should eventually grow out of the biting stage but you can do some things such as what I mentioned above to deter and stop the puppy biting.