Well, the Earth is a big place, and there are a lot of radioactive elements of varying degrees of radioactivity distributed throughout it. To eliminate the radioactive materials, you either have to get rid of them, or make them somehow stop being radioactive. Uranium and thorium ores in the ground are mildly radioactive and sending all that rock into space wouldn't make sense. A more pressing concern is what to do with nuclear waste generated as a byproduct of weapons manufacture and nuclear power plant waste. Currently the best ideas are just to put the wastes somewhere where people won't go, and away from water that people end up drinking, while waiting for the materials to decay (tens, perhaps hundreds of thousands of years -- it's a tough job trying to predict how a geological formation will behave in that long a time).
An idea of Carlo Rubbia's (co-discoverer of the W and Z bosons at CERN) is to fire a beam of protons at radioactive waste, breaking the heavy nuclei up into lighter nuclei. These ligher nuclei will still be radioactive, possibly more so than their parents, but will have shorter lifetimes and will decay away quicker. They may even be useful for power generation. I'm not sure if this idea is anywhere even close to break-even for the power you put in vs. what you get out, or economically close to being viable, so it too may not make sense.
You probably don't want to eliminate all radioactive elements from the earth. Some are used for power generation, others for nuclear medicine as radiotracers. Other uses include making nuclear weapons and depleted-uranium shells which can penetrate armor. People complain about the radioactive residues of both of these kinds of weapons after they are used, and yes, it's hard to get rid of them.
On the more fanciful side, if you magically turned off all radioactive decays everywhere on earth, the earth would likely freeze over. The interior of the earth is very hot, and constantly loses thermal energy to space. This heat is generated by radioactive decays. It may not be much of a perturbation on the global surface temperature, but if current climate studies say anything, it's that a few degrees of average temperature can have a catastrophic effect. Once you get a significant portion of the earth covered in ice, it looks white and reflects sunlight, cooling even more, plunging further into an ice age. Of course it looks as if we are headed in the opposite direction, and it's impossible just to switch off radioactive decay.
(published on 10/22/2007)