Let's not fight over this guys! Throughout history we've left messes for future generations to "clean-up." It's unpleasant, but par for the course. Clearly radioactive waste is something else. It's funny, if the ancient Greeks had developed nuclear power we'd still be looking after the waste wouldn't we? Makes one think doesn't it?
It's funny, if the ancient Greeks had developed nuclear power we'd still be looking after the waste wouldn't we?

No more than we have to take care of the ruins they left us.

From Wikipedia:

The radioactivity of all nuclear waste diminishes with time. All radioisotopes contained in the waste have a half-life - the time it takes for any radionuclide to lose half of its radioactivity. Eventually all radioactive waste decays into non-radioactive elements; for example, after 40 years 99.9% of radiation in spent nuclear fuel disappears [1].

http://en.wikipedia.org/wiki/Nuclear_waste

After 2000 years the radiation of nuclear waste would be 0.000000000000000008% of the initial radiation. Million times lower than the natural radiation level. Or you want to shield our kids from the natural radiation too?

Which just goes to show that you should not accept everything you read on Wikepedia uncritically.
Nuclear waste consists of many different isotopes such as U238 with a half life of 4.5 billion years and several isotopes with very short half lives.  These are not the problem.  It's the isotopes with intermediate half lives such as the biologically active strontium 90 and caesium 137 with half lives of around 30 years that require future generations to ensure that our wastes are kept isolated for thousands of years.
It seems you are not aware what the term "half life" means. In 1000 years an isotop with half life of 30 years would represent   1/2^(1000/30) ~ 9.10^-11 or one ten billionth of its initial amount.

Considering that isotops like the one you mentioned are some 0.1% of the nuclear waste it would turn out that if you decide to eat (!) 1 gram of 1000 old waste you would receive some 10 million atoms of radioactive stroncium in your organism.

In comparison only the naturally occuring radioactive C-14 staying permanently in your organism is 1,505,000,000 million atoms and you don't seem to die from it, right? Do you have any idea how much radioactive materials you breath every day from emissions from coal power plants and from car exhaust? I guess you don't but if you make the research don't try not to breath - it can be dangerous.

OK, I figured out that to be factually correct I have to account for strontium-90 being 200 times more radioactive than C-14. This makes it that you already have 7,525,000 million atoms of strontium-90 equivelent in your body only from the C-14. The actual value of naturaly accuring radioactive isotops  in everyone of us would be much higher.
Reality rather than wishful thinking:
http://archive.greenpeace.org/mayak/
But if you don't want the Greenpeace view you could take it from the US Nuclear Regulatory Commission:
"Some of the radioactive elements in spent fuel have short half-lives (for example, iodine-131 has an 8-day half-life) and therefore their radioactivity decreases rapidly. However, many of the radioactive elements in spent fuel have long half-lives. For example, plutonium-239 has a half-life of 24,000 years, and plutonium-240 has a half-life of 6,800 years. Because it contains these long half-lived radioactive elements, spent fuel must be isolated and controlled for thousands of years."
http://www.nrc.gov/reading-rm/doc-collections/nuregs/brochures/br0216/r2/index.html#how_hazardous_hl w
That's why more technologically "advanced" nations like Russia are separating long-lived transuranic elements and are reusing them as nuclear fuel.

Don't get me wrong - the nuclear waste problem is not to be underestimated. But it is largely technically solvable and in many countries is successfully solved. The reason it is not solved sufficiently in western countries is just one - NIMBYSM - and your attitude shows exactly that. For example there are billions accumulated for that storage in Yucca Mountain and still the problem is protracted because some people don't have other purpose in life than denying everything and everywhere.

"Reality" and "Greenpeace" are grossly incompatible words.

And digging out Russian stories dating from Stalin's time is a bright proof for that. Where are the same stories for USA, France, England, Germany? They also store nuclear waste, and much larger amounts BTW. Or you feel nostalgic for early Soviet's Russia? I don't.

So, where are the mutating children, where are the terrorists making dirty bombs and enriching plutonium in their basements? Where?