The average person is exposed to 170 millirems of radiation per year. 50% of that comes from natural sources (cosmic rays, solar radiation, upper atmosphere radiation, and natural radioactivity), while the other 50% from artificial sources (mostly from medical exams).

Radiation is measured in RADs (Radiation Absorbed Dose), REMs (Roentgen Equivalent Man), Gy (gray), Sv (sievert), or Bq (becquerel).

Radiation statistics (mostly from http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html ):

A person would get one millirem of radiation from:

You increase your dose by a millirem by:

The risk of one millirem of radiation dose is a 1 in 8 million risk of dying of cancer if large dose effects extrapolate linearly to zero dose.

The loss in life expectancy from a 1 millirem dose is about 1.2 minutes, which is equivalent to:

Typical annual exposure levels in millirem:
   5 statutory limit on radiation from operating
     a nuclear power plant
  25 internal exposure from radioactive
     material ingested into the body 
  45 cosmic rays
  75 diagnostic medical exposure (x-rays)
  60 external radiation from radioactive
     ores, etc
 120 natural radiation sources (combined)
 200 average total exposure in the U.S.
 500 average occupational dose for radiologists
1250 natural exposure in mountainous regions of Brazil
5000 maximum permissible occupational exposure (5 rem)
Consequences of radiation exposure in rem (not millirem!)
  rem    Effect
  0-25   No observable effect  
 25-100  Slight blood changes 
100-200  Significant temporary reduction in blood
         platelets and white blood cells
200-500  Severe blood damage, nausea, hair loss,
         hemorrhage, death in many cases 
   >600  Death in less than two months for over 80% 
         of people