In forms of harmful ionizing radiation, (i.e. neutrons gammas) none. They do give off other forms of electromagnetic radiation primarily in the form of microwaves. These waves do not have enough energy to ionize atoms, however, there are skeptics out there that say there can be harmful effects from long-term exposure to these other forms of non-ionizing radiation; definitive results are hard to come by due to lack of data and poor correlations. In my professional opinion as a nuclear and radiological engineer, there is nothing to worry about from the EM radiation emitted from a computer. The low intensity and energy of the microwaves from a laptop wouldn't be able to cause any damage to cells. Radiation (ionizing and non-ionzing) are around you all the time. From the light you see, to the natural background radiation you get everyday from natural sources. It doesnt do us any harm-the human body is very resilient.

However, if you feel that you do need protection, then a lead apron from a dental office would more than suffice although I would suggest looking into Faraday Cages as a possibly more economical (and comfortable!) approach to blocking out EM.