Suppressors (silencers) are legal at the Federal level, but are highly restricted and taxed. It is the state level where suppressors are sometimes banned outright. So, whether or not you can own a suppressor often depends on the state where you live. Here is a chart which shows what states generally allow suppressors, machineguns, short barreled shotguns and rifles, or "Any Other Weapons" (AOWs).
Some of the states on this list have further restrictions on who can own these items. For instance, I believe at least one state on this list that is shown as a "Y" for suppressors, only allows Law Enforcement personnel to own them. Do your research, find out the laws in your area!