They collect radioactive dust (I think polonium that results from the decay of radon) out of the air (it seems to be charged).
If you wipe the entire face of a CRT that has been used a lot recently, with a tissue (preferably held in such a way that the dust all collects in a small area of the tissue) then hold this dust in front of a geiger counter, it will be quite noticably radioactive.
By collecting this radioactive dust out of the air, some of it will be prevented from lodging in my lungs.
I suspect that the replacement of CRTs with LCDs in households will eventually result in an increase in lung cancer, though probably only a small one that may be masked by other changes over the years such as vehicle emissions.
Here is some info about the dust: