The way we perceive sound and the specific properties a sound might have depends a lot on the environment. A common way to change the way sound is perceived is to add sound absorbent materials to a room. Since many different types of material are needed to cover the wide range of usages and environments needed for sound absorption, there is no one particular type of material that is the best. There are general properties that the best sound absorbers have, regardless of material.
Sound is a pressure wave that can travel through liquids, solids and gases. The vibrations of a sound wave interact with your eardrums, which are then translated by your brain into sound. When a sound wave encounters any surface it interacts with it in three ways. It can transmit through the surface, it can be absorbed by the surface and it can be reflected by the surface. The specific levels of each interaction type depend on the material encountered. For instance, a solid surface such as concrete will absorb little of the sound and reflect most of it away.
Porous sound-absorbent materials will be anything that can transmit sound through themselves and then absorb the sound, converting it into a small amount of friction energy. These can be items such as carpet, heavy draperies and open-cell foams. Any item that will allow air to pass into it and then be absorbed by a cellular structure will make a good sound absorber. The best porous sound-absorber materials will be specifically made for sound absorption, such a thick foam pads or thick sound-dampening window drapes.
Another way sound can be absorbed is by allowing the material to flex and reverberate, effectively absorbing and dissipating the wave. This is done with flexible panels such as thin wood or other non-rigid material suspended in a frame. Any large surface that has the ability to resonate with any sound that interacts with it can be used as a panel sound absorber. Panel materials are generally better at absorbing lower frequencies then porous materials.
Too much sound absorption can be a bad thing. Without a small amount of natural reverberation that comes from reflected sound waves, sounds will have a dead or flat quality. Also, be aware that some sound-absorbing materials will absorb certain frequencies more than others, such as thin wood panels absorbing more of the lower frequencies. If are looking to use soundproofing as a means of creating a better environment for music, for instance, then wood panelling may rob the sound of a lot of the bass, creating a very flat experience.