He's doing it because it's fun Stop making it fun. Remember, negative and positive attention are all good things in a puppy's mind. A stern "NO!!" sounds as happy as a "Aww, look at my cute puppy wuppy puppy!".

Rather than driving you both insane, simply leave the room whenever your puppy starts nipping you for play. If puppy tries to instigate a nipping/playing session, say "NO" and leave the room. When you come back into the room, give the puppy a stuffed toy and play with him that way. If he ever puts teeth to skin, say "NO" and leave the room again.

(and yes, it is normal for puppies to put EVERYTHING into their mouths. They're like young toddlers and explore with their teeth!)