Somebody: According to the U.N., the world average is 2.4 millisieverts per year:
http://www.unscear.org/docs/reports/gareport.pdf
However, this seems to vary from place to place a great deal. The same document says that natural background radiation can be anywhere between 1 and 10 millisiverts per year. According to here:
http://www.bbc.co.uk/news/health-12722435
Australia naturally has only 1.5 millisieverts per year background radiation, while North America has twice that at 3.0 millisieverts.
Other sources seem to converge on these figures:
"Radiation level: The average person is exposed to 2 to 3 millisieverts of background radiation per year from a combination of cosmic radiation and emissions from building materials and natural radioactive substances in the environment.
The U.S. Nuclear Regulatory Commission recommends that beyond this background level, the public limit their exposure to less than an additional one millisievert per year. The U.S. limit for radiation workers is 50 millisieverts annually, although few workers are exposed to anything approaching that amount. For patients undergoing medical radiation there is no strict exposure limit—it is the responsibility of medical professionals to weigh the risks and benefits of radiation used in diagnostics and treatment, according to Langhorst. A single CT scan, for example, can expose a patient to more than one millisievert."
http://www.scientificamerican.com/article.cfm?id=how-radiation-threatens-health