For many years we heard the promises of nuclear power. "So cheap it wouldn't even be metered!" is the one I remember. We have yet to realize that dream. We are beset by the hazards of radioactive waste and accidents at the plants themselves. Yet it is possible with existing technology to have unlimited safe nuclear power.
This can be accomplished by the use of a radioactive material that decays into a non-radioactive waste product. This material should not emit any gamma radiation, therefore it would be easy to shield. Such a material exists. In fact it is quite common with many tons in our atmosphere. This material is Carbon14. It decays with the emission of an electron. Once the electron is emitted from the nucleus, it becomes Nitrogen14.
Carbon is quite active biologically, but if it is bound up as Titanium Carbide, it is very inert and is also a refractory material that cannot be easily decomposed. As the Carbon14 turns into Nitrogen14, the material gradually changes from Titanium Carbide to Titanium Nitride which has very similar physical characteristics.
This type of nuclear power source produces power at a constant rate and cannot be made to react any faster or slower. It very gradually loses it's reactivity, decreasing about 10% in 1000 years.
A thin coating of Copper would completely shield the material so that the fuel elements could be safely held in the hand. A fuel element with the shielding removed wouldn't be very hazardous since the radiation would be stopped by a few inches of air.
This material would have to be made in an ordinary nuclear reactor, but since the material itself is so safe and easy to transport, the reactors could be at a remote site. They could even be on the moon.
For more details please see Energy for the Millenium
The real problem with nuclear power is that enriched uranium is very inexpensive. That means that there is no monetary incentive to burn the waste products since it is cheaper to just buy more uranium and produce more radioactive waste.