Lots of specific answers here, all addressing one or more parts of the problem. To help newbies and not so newbies alike, let's look at the overall problem.
Noise (and hand shock) is caused when the energy in the bow/string/arrow system is not absorbed completely during the shot. When you draw your bow the energy is stored in the limbs. When you release the string the energy transfers from the limbs to the string to the arrow, and eventually to the target. After the shot any excess energy follows the reverse path back to the string to the limbs and then to the riser and attached accessories. Noise is caused by those parts vibrating like tuning forks due to the excess energy.
To solve the noise problem you can do one or all of the following to make changes to the riser, limbs, string, or arrow. They all help to absorb the extra energy that doesn't go into the arrow when it is shot:
~ Use a bow with more mass in the riser, not in the limbs, to absorb excess energy. You want low mass limbs to maximize their speed. The extra mass in the riser will help absorb excess energy which would cause vibration and noise.
~ Use a stabilizer to add mass to the riser. Stabilizers are designed to help balance the bow and keep it from leaning forward or backward or from side to side. They can also help absorb excess energy which can turn to vibration or noise. As for certain stabilizers having special noise dampening qualities, take that with a grain of salt and think about if the claims make sense or if they are just marketing mumbo jumbo. A long threaded bolt screwed into your accessory mounting point could work just as well and cost you a fraction of the price.
~ Add pads or silencer materials to the bow limb where the string contacts it during the shot. This will help reduce the slap you hear.
~ Use string silencers, anything that is relatively lightweight that will absorb the vibrations. This can be cat whiskers, bits of fur, yarn puffs, or even pieces of rubber or leather attached to the bowstring. Position on the string is important too; you want to place your string silencers where the harmonics/vibrations on the string are the loudest. On a recurve or compound, that point is often half way between the nock set and where the string touches the limb, on a longbow it is about a quarter of the way up from the contact point to the nock set location. Your specific position will vary with the bow.
~ Use an arrow with more mass (i.e., heavier); more mass allows more energy to be absorbed by/transfer to the arrow for its flight downrange. The easiest way to get more mass, if your arrow is stiff enough, is to go with a heavier broadhead. It adds weight and increases your FOC which has inherent benefits for good arrow flight; the front of the arrow is pulling the back of the arrow rather than the back of the arrow pushing the front. If you arrow doesn't have the necessary stiffness to add weight up front you can go with heavier arrows instead; you can adjust the arrow weight, length, and broadhead/point weight to get what you want.
~ Make sure the connection points between pieces of your bow (limb to riser, quiver to riser, arrow rest to riser, etc.) are tight and have not worked themselves loose, which will cause vibrations or banging noises.
So, in summary, make changes to the riser, limbs, string, or arrow to reduce excess energy, which equates to noise, when you shoot. There are lots of ways to do each of these things and many of them are simple and inexpensive.
Good shooting,
Larry
. 
