During the 90s there was a concern that radiation form monitors can be very harmful, especially for a pregnant woman. Because of this concern many companies decided to limit the amount of radiation from monitors, as they did not want them to be portrayed as dangerous. This was in the era of CTR monitors which were very big, and that is why they might have seemed so dangerous.
Currently, people are using flat TFT/LCD monitors, which use less wattage and are a lot lighter. The current research indicates that there is no real danger from monitors and this includes both CTR and LCD. It seems that we may have overestimated the dangers, but I suppose it is better to be safe than sorry. The reason why there was a concern about CTR monitors is that radiation travels through everything, including walls, flesh, or even screen filters. The fact that monitors continue to emit radiation even after they are switched off was also a major concern. It is fortunate that the recent data suggests no ill effects from monitors, especially TFT/LCD monitors which are being sued by people these days. Of course, staring at the monitor all day might make your eyes tired, so that that into account. Make sure you have regular exercise and take breaks as often as you can.