Playtime Aggression

Owners of new kittens can be easily identified all too often – all you have to do is look at their hands. Kittens are notorious for attacking hands during playtime, and those tiny teeth and claws can and do leave marks on delicate human skin.
Some owners take pleasure in this form of play, at least while the kitten is young and the game is still relatively painless. As kitty grows, in a matter of weeks, many owners find that the cute game is becoming too painful. It's time to teach the kitten to stop…
It should be stated at this point, that as with any behavior trait, consistency is the key. Therefore, you would be advised to avoid any aggressive interaction between your hands and your kitten, as young as she may be. It may look cute now, but soon enough it will get nasty and you'll have a bad habit to deal with.
The Reasons for Feline Playtime Aggression
Your kitten is not being "bad". When playing, all young mammals imitate some form of adult behavior that will be useful for them as they grow up. With kittens it is either hunting or fighting. Watch a litter of kittens tumble around on the rug and you will see the same type of playful aggression displayed between them. It is their way to practice hunting and fighting routines which nature intended them to use as adult cats.
Clearly, there is nothing wrong with aggressive play itself. The problem begins when the target is delicate human hands. The solution lies with redirecting the aggression to more suitable targets.
Adding a Playmate for Your Kitten
Another kitten can make the perfect target, or rather partner, for aggressive play. Protected by their furry coat, kittens seem to know their own boundaries and thresholds and there is usually no need to intervene in their aggressive play.
Obviously, the decision to take in a second kitten is more complex than that. You are not getting a toy for your kitten, but rather committing yourself to taking care of another feline, for decades to come. However, if you can provide a home for another kitten, remember that in terms of kitten behavior, raising two kittens is actually easier than raising one. They keep each other occupied and make the best playmates for any kind of kitty play, aggressive types included.
Redirecting Playtime Aggression to a Toy
A cat toy makes a perfect outlet for all that pent-up playful aggression. Use fish-rod like toys to initiate interactive play sessions with your kitten. This is a great way to interact with your cat while keeping your hands out of reach.
Use a variety of toys, whether bought or homemade, but make sure that they create enough distance between kitty and your hands. Rotate the toys and keep them out of reach when you are not playing with your kitten. This will keep them fresh and enticing when you do bring them out (and it may prevent your kitten from getting entangled in any strings while you're away).
How to Release Your Hands
Your fingers are indeed tempting. With a vibrant kitten, or even a cat, it's sometimes too easy to find your hand held tight by teeth and claws. Often, they will not be penetrating the skin, but painfully close to that point. Your cat is likely to be extremely excited at this point and hold tight, not letting go of his coveted prize.
Here's what you should NOT do:
Do not try to pull your hand away by force. When prey tries to escape, a feline's instinctive response is to tighten its hold. You could end up with painful scratches and even bites.
Do not shout or yell at your cat. They are not thinking clearly at this point, and you may aggravate the situation and turn this into fear induced aggressive behavior.
Never ever hit your cat. Not in this situation or any other. If you do, you will end up with an even more aggressive cat, and a stressful episode for both cat and owner. Next time, your cat is even more likely to bite and scratch - this time out of fear as well.
Here's what you should do. Relax the hand that is held by the cat's teeth and claws. Stay calm and avoid direct eye contact with your cat. With your other hand try to grab a toy or some other object and distract your cat's attention with it. If possible, make some playing moves with it, in an attempt to make the cat let go of your hand and move on to chase its "new prey".
If you are unable to reach any suitable object, use your free hand to create a diversion. Tap on something, or make some scratching noises on some fabric. Make the cat lose interest in its "current prey" (your caught up hand) and focus on the new attraction.
Wait for your cat to at least loosen its grip on your hand, preferably let go of it entirely. Once you are sure you can remove your hand, move it out of reach in a swift movement.
Break away from your cat at this point and allow for some cooling off time before you engage in any form of play again.
Be Consistent
Do not allow playful aggression in any form. Whenever your kitten directs her aggression towards you, be it your hands, ankles, or any other body part, use the method described above to break away. Do not allow aggression play when your hands or feet are under the covers either.
Remember to provide your kitten with alternatives – either by bringing in a second cat into your home, or by using cat toys. Keep in mind that this is natural behavior for kittens and young cats. They are more than likely to outgrow this phase at some point. Handle this correctly, without ever shouting at or punishing your cat and you should be able to make it across kittenhood with your skin intact.

Source: The Cat Site