This is just from a translated webpage, but apparently the Japanese Society of Radiation Safety Management did some experiments after the earthquake with readily available household products to see if they could filter out the radioactive particles from water. They used the common pitcher-style water filters many of us have sitting on our kitchen counters, and found that they removed a very high percentage of the particles.

I read this here.

Certain radioactive isotopes will actually dissolve in the water (I believe radioactive iodine falls in this category) and which requires other methods to remove from water, such as ion exchange.