Another question to start may be "should" you stop play biting. I know it is annoying and it is critical as a result to RE-FOCUS your puppy's biting so that he doesn't got for pant legs etc. The advice to stop moving, and making him stop so it isn't a game is good - but never reprimand for using his mouth in general.
I see dogs every day with horrible social skills - their play skills with other dogs are poor and so many dogs today end up with bite histories. All of this is related to poor bite inhibition and this is caused by erroneously teaching puppies not to ever use their mouths. It is SO CRITICAL that all puppies learn effective bite inhibition, which just means that they get good experience in using their mouth to understand the power of it and strength of their bite - these dogs, even if they develop other issues such as fear or aggression, are far more trusted to not bite or be too rough with kids.
Dogs are not born with soft mouths, but they are hardwired to easily develop the ability to bite softly and gently. The key is to develop this knowledge in your dog, not just turn it off so that he remains stupid to his mouth strength.
So I strongly disagree with any advice to yell NO, or use other aversive methods to discourage the behavior. Instead, focus the behavior where the puppy can learn the impact of his actions safely and properly. The right conditions mean giving plenty of feedback about bite strength.
I always allow my young puppies from the age of 2-4 months to mouth on my hands and arms - as soon as it is too hard, I yelp and show them pain. Most puppies learn this and stop, gradually learning to be softer and softer. Other dogs are also excellent at teaching this and finding good adult dogs with excellent social skills who also are willing to properly discipline are key. These dogs will growl and verbally discipline puppies for inappropriate behavior and are the best teachers - they should be encouraged. I have one of these adults in my home and several trainers bring their socially challenged puppies over to be "schooled" by my adult girl.
I also provide lots of tough toys to exercise their natural biting and mouthing instincts - dogs should never be taught it is bad to bite or chew. They should be taught what they can bite or chew, and what they can't or shouldn't. Chewing is a natural dog behavior and mouthing is a natural puppy behavior as they learn and explore with their mouths. I provide my adults with raw meaty bones to exercise this chewing desire and they have never been inappropriate with anything or anyone else. Puppies learn the strength of their mouth so they can be trusted not to every use it improperly.
Just try to remember that these are dogs - not people and we must remember to allow them to be dogs and not put human expectations on them. You will have a more trustworthy dog if you do.
Here is an excerpt from Jean Donaldson's Culture Clash:
"Smart puppy owners allow some puppy biting in order to give the puppy information on his own strength. Puppy biting is such a valuable thing, in fact, that puppies who do not play bite should be actively encouraged to do so in order to develop a soft mouth. Start off by targeting harder bites. Let the puppy chomp away on your hands, and monitor the level of pressure. Although puppy teeth are sharp, puppy jaws are undeveloped, so this should not be unbearable. As soon as the puppy bears down a little harder, screech OUCH as loud as you can and as though it hurt much more than it did and look at the puppy like he is an ax-murder and leave the room for one minute. This time out is a clear refusal-to-play consequence that goes with the OUCH as the conditioned stimulus. After the minute has passed, return and resume. He may be more prudent temporarily, and he may not. Be prepared to repeat this process over and over, depending on your individual puppy. Puppy always learns eventually that if puppy bites too hard, puppy plays by himself. It is more beneficial if multiple people implement the process for optimal learning (the exception being young children - young kids and puppies are an extremely dangerous combination).
When the puppy has consistently demonstrated some greater self control, you may start targeting even moderate pressure bites. The reason for doing this in stages is that the puppy will be unable to comply if you set too high an initial criteria. Little biting-maniac puppies can and do learn to hold back on hard bites, but they are simply unable to hold back on all or even most bites too early on. You're teaching him self control in manageable chunks and when he is mouthing you with little pressure, you can then teach him a "don't touch" command and redirect him to appropriate bite sources such as toys. At this point, he now knows that he may not bite humans at all, and you've got the critically important benefit of acquired bite inhibition." Pages 67-69
