Exposure damage to radiation is additive over your life. Basically you want to avoid it whenever possible.
As a blanket statement, this is incorrect.
There is a strong body of evidence that long term exposure to low levels of radiation has positive benefits on the cellular level in protecting against cancers. Long term studies of nuclear workers dating back as far as WWII shows that they have significantly less cancers than the general population.
This statement is way to simple to describe the biological effects of exposure to ionizing radiation.
I don't really want to go into it, but what most people should be interested in is low level radiation over a long period of time. The scientific studies of low level radiation (<~5 R/yr) are inconclusive. Due to this two theories on its effects have been created and are being tested as data accumulates (which is very slowly).
The first theory states that any amount of radiation will cause biological damage and that logically the longer and more intense the exposure, the greater the damage. This theory has made the nuclear industry formulate the ALARA (as low as reasonably achievable) standard. Radiation doses are minimized and workers cannot exceed a certain amount of exposure per year (5 rem). This theory was interpolated from high level short term exposures to ionizing radiation. There is little proof that it is justified, but it is agreed that it is at least conservative.
The second theory is that ionizing radiation is only harmful above a certain threshold and may be helpful below that threshold in a complicated manner. This is because cancerous or damaged cells that absorb radiation have a higher probability of dieing than normal cells. At a certain radiation level you will create as many cancerous cells as you kill. Below that level you will kill more cancerous cells than you create (though it depends on the amount of cancerous cells and other cancer producing rates). Because this is low level radiation, the non-mutation deaths of normal cells by radiation is not factored in because it is insignificant (you can think of cancerous cells as an amplifier to biological damage from radiation whose value is many orders of magnitude greater than radiation cell deaths). For this reason, there may be a non-zero low level radiation dose rate that depends upon how many cancerous or damaged cells that you have that will be more healthy for you than a zero radiation dose rate. This theory has some scientific backing, but is certainly not conclusive yet.
I tend to agree with the second theory more because I can relate it indirectly to things like radiation treatment. Radiation treatment uses ionizing radiation to kill tumors by focusing it at a specific area of the body. Both normal and cancerous cells in that area are hit. The cancerous cells die and the normal cells are injured, but recover. The overall result is that a patient has a higher probability of surviving.