It is legal to use a public proxy to access the Internet, according to Public Proxy Servers. However, it is illegal to use proxies to access websites from which one has been previously banned or to access illegal content.
Any activity that constitutes unauthorized access to a website is illegal, according to bit-tech, quoting a ruling by a U.S. Court in Craigslist vs 3Taps. Public proxies that mask or allow users to switch IP addresses may be deemed to fall into that category, as the Computer Fraud and Abuse Act is not explicit on the matter, states bit-tech. The ruling, however, criminalizes access to a website through a proxy after having been banned from said website.