Even agencies with networks connected to the Internet are likely to be safe, as worms are far more rare than viruses or Trojans. There are more hoaxes than viruses. In fact, given how fast and far emailed hoax warnings can spread, the hoaxes waste more total time than most of the viruses do. If you get an email warning of some particularly nasty virus, and it tells you to immediately pass the warning on to everyone you know, don't . Check it out first.
Most antivirus companies maintain lists of hoaxes on their Web sites.
Even the various urban legend sites have lists of the more widespread hoaxes. If you do feel compelled to pass on a virus warning, do your homework first, and make sure your email includes Web addresses of documented evidence of the authenticity of the virus. As the state of the art advances in software development, and operating systems become more sophisticated, viruses are getting more sophisticated as well. Stealth viruses hide themselves from virus scanners. Yes, antivirus programs are just programs, and they're not immune from viruses, either, although they take precautions to avoid or detect infection.