Property rights are the rights to own and control resources. In a capitalist society individuals own rights to property privately, whereas in a socialist society rights to property are owned by the government and distributed or maintained by officials. In the United States we have both private property (televisions, refrigerators, cars, etc.) and public property (water, national forests, rivers). In some circumstances property is controlled both by private rights and public policy, often in the form of price controls or mandates on disposal of certain chemicals.
I'm a libertarian, and as such I believe that private property rights should be entirely binding and enforced by the government. Libertarians only insist that individuals be allowed to act in whatever manner they choose, provided they do not interfere with the equal rights of others to live however they may choose. If the government were to own property, they would not necessarily be violating the rights of an individual. However, it is when the government gets involved with the voluntary contractual agreements of individuals that government begins to violate the libertarian principle. There are many other ways the government of the United States violates property rights, but most striking is their use of coercion to confiscate property.
Consider that the police are allowed to confiscate a person's property without any sort of trial, conviction, or even indictment. In Louisiana County, Florida the police describe as carrying more than $100 as "suspicious behavior" and use it as justification for seizing that property. They also seize other valuables like jewelry, and even cars. Of course this is entirely coercive, as resisting a seizure will incite the officer to use force for the seizure, and resisting at that point could result in your own death.
Police can confiscate a person's car, house, or any of their possessions without any sort of legal trial or conviction. Police can confiscate any amount of money that has drug residue on it; according to a 7 year study by toxicology consultants fully 96% of bills in America tested positive for cocaine residue. In fact, a series of studies completed for the U.S. Bureau of Engraving and Printing reveal that at minimum 15% of the government presses that print our currency are contaminated with cocaine.
Under the Comprehensive Forfeiture Act of 1984 and other federal crime laws, any money an attorney receives may be confiscated if the government alleges that they were proceeds of an illegal transaction. In March 1992, the Securities Exchange Commission froze all of the assets of the law firm Kaye, Scholar, Fierman, Hays and Handler. Facing imminent bankruptcy, the firm paid $41 million to have their assets unfrozen. The government's claim was that the firm has concealed information from prosecutors about their clients, despite attorney-client privilege being an establish practice of the law community.
Of course as a libertarian I believe that this is wrong. The government should not ever use coercion except in the circumstance that coercion is already in use by other parties. In the United States, despite property rights being assigned through private means, the government still has entirely legal use of coercion to confiscate individuals' property.