The other day I was talking with a friend about sound suppressed weapons found in video games. (The use of the term "silenced" is technically incorrect, yet commonly used.) I was surprised to find that my friend, as well as many other people, believe that it is illegal to own such weapons. This is not very accurate.
The National Firearms Act of 1934 established definitions of, and laws regulating, several classes of extra effective weapons such as machine guns, short barreled shotguns and rifles, and sound suppressed weapons. It was passed shortly after the repeal of Prohibition, to deal with a growing number of heavily armed gangsters. The only real group of un-ownable weapons is that a modern addition has made it impossible to own machine guns manufactured after 1986, through a legal trick where they make it illegal to sell/transfer such weapons to other people, but not directly make it illegal to own.
In order to own these types of extraordinary weapons, commonly known as Class 3, all you have to do is pay a $200 federal tax to transfer the weapon to you, fill out a bunch of paperwork, submit to a background check, and wait.
Sound suppressors cost $250-2500, depending on the make, model and caliber of weapon it works on. A typical price is in the $600-900 range, not including the $200 transfer tax or accessories. You'll usually need to have the barrel of the weapon threaded, which will cost about $100, or buy a pre-threaded replacement or adapter. You can always use a single suppressor on several firearms of the same caliber, and some suppressors are even capable of working effectively on a variety of calibers!
People often wonder how quiet suppressors are, which is understandable considering most people have little reason to have ever seen one in action. They aren't like in the movies and video games, which show them making whisper-quiet "laser" sound effects. They also typically do less obvious things, like change the pitch of the shot, as well as change the actual noise thus making it sound like some other non-gunshot event. However, a useful comparison is to note that most suppressors reduce the decibel level of the muzzle blast by 34-40 dB, and most shooting hearing protection reduces the heard sound level by 18-32 dB. That effectively means that you can often shoot a suppressed weapon without wearing hearing protection, and that it will sound like a regular gunshot while wearing hearing protection.
If you're interested in finding out more about suppressors, here are some of the major current manufacturers, in alphabetical order: