Not by itself. The type of radiation given off by nuclear waste is not visible to the human eye. However, there are certain materials called fluors or scintilators that will absorb the radiation and re-emit it as visible light. If you mix a radioactive material with a fluor, it *will* glow by itself. For example, the hands of a glow-in-the-dark watch are painted with such a mixture. Don't worry about getting radiation poisoning from your watch, however; the amount of radiation given off is very small.
Radioactive material that is stored close to glass or water can emit Cherenkov radiation. This is what happens when radioactive particles travel through a material faster than light can travel through *that particular material* (keep in mind that *nothing* can travel faster than light in a vacuum, which means that Cherenkov radiation can never be created in a vacuum). Cherenkov radiation is usually pretty weak, however, and requires special equipment to detect.
There is *one* other way in which a radioactive substance might glow. Each radioactive decay event liberates a tiny amount of heat. If you have a large amount of a *very* radioactive substance, it might actually heat itself enough to glow red hot. Radioactive waste from, say, a nuclear power plant usually doesn't get hot enough to glow in the visible spectrum, although it is a strong emitter of infrared.
I hope that helps. Good luck!