Radiation hormesis: contradicts all we know about evolution, can be shown false with elementary physics and math.

See Radiation hormesis. This thing is on the rise (just like intelligent design), with potentially grave direct consequences if some nuclear regulatory body accepts this 'theory' and relaxes nuclear pollution standards - and similarly grave consequences if nuclear power opponents pick up the idea and use it their way, hints at which you can see in this wiki article ("In all likelihood, recognizing that low dose effects can't be predicted from high dose experiments would force a strengthening of public health standards, not their weakening, as hormesis proponents would argue.").

Putting aside that hormesis is just a new name for old bullshit (see quack medicines of early 20th century. Radium toothpaste, uranium ore teapots, you name it), there's outline of what is fundamentally wrong with "hormesis theory":

Firstly, according to the understanding of evolution, a wholly beneficial "defense response" does not need to be switched off in absence of ionizing radiation. Even more, the 'switch', even if present, very quickly goes away if it is not needed. For real biological examples of this see permanent tan in blacks (tan doesn't switch off in absence of light, because in tropics you always need tan), lactose tolerance in whites (lactose production doesn't switch off in adulthood). Those are just 2 most obvious examples, which are also examples of very quick evolution that happened recently in the history of homo sapiens. I'm sure there's a lot of more obscure examples in animals; I am not really a biologist.
(It's interesting that hormesis proponents love to refer to tan as example of defense response triggered by radiation. Well, used to. Hopefully, with election of Obama, whites will stop defining 'human' as something which produces melanin mostly in response to sunlight)

Secondly, humans today are exposed to about same level of radiation as in the past - or higher because of sealed homes and radon (in case you want to talk about cavemen, don't bother. Caves were never the primarily habitat of humans, nor are habitable caves well sealed. Bones are found in caves so much because bones preserve in caves a lot better than outside caves).

Thirdly, it wouldn't be a problem for living organisms to evolve to concentrate naturally radioactive elements, had those been so beneficial. Seriously, there's enough naturally radioactive elements around. Better yet, cells are producing some free radicals all by themselves without any ionizing radiation.

But okay, let's just follow less sophisticated of radiation hormesis proponents and speculate that radiation in small doses produces some chemicals that are required for some cell metabolism.
After all, cellular machinery being complex it seems very reasonable that cell's response to radiation would be nonlinear... or does it? A single cell wouldn't make good particle counter... it is, after all, very tiny, and rarely gets hit by ionizing particle or gamma ray photon. How bad of a Geiger counter a cell would be, you might ask? Turns out cell sized Geiger counter would be far worse than I would have thought.

Did you know that you have on order of hundreds times more cells in your body than you absorb ionizing particles in a year, at background radiation level? I didn't know, but fortunately it is quite easy and straightforward to calculate number of particles (of specific type) that your body absorbs when you get specific dose.
From the definition of Sievert, the general formula for number of particles for given dose is:
Number of particles = (Dose in Sievert / Q factor) * body mass / kinetic energy per particle
Background dose is 2.4E-3 Sievert per year. (http://www.unscear.org/docs/reports/gareport.pdf)
Let's take body mass as 80kg.
For 1MeV soft gamma ray photons (Q=1), the max number is:
N = 2.4E-3 J/kg * 80 kg /(1E6 electron volt) = 1.2E12
About hundredth of number of cells in your body, which is estimated as 1E14
Let's redo the calculation for Radon's alpha particles, of which you need much smaller number for same 'dose':
N = (2.4E-3/20 J/kg) *80kg / 6E6 electron volt = 1E10
That's some ten thousands times fewer alpha particles than there are cells in your body.
The cells which suffer impacts to the cell nucleus are even smaller percentage.
Alpha particles usually stop within a few cells. Gamma photons ionize when they get scattered, meaning that gamma photon doesn't just rip through your body ionizing stuff on its path, but delivers focal damage at few spots. The bottom line is, individual cell is very rarely affected by background radiation at all.

I hope it should be fairly obvious that there couldn't be any 'nonlinear' response of individual cell to such rather low probability of it getting struck by gamma or alpha particle during its lifetime. It either gets struck and has response, or it does not, and has no response. Probability is by definition linear. Only at the doses approaching 1 Sievert, a significant portion of your cells would be struck by ionizing particles [that's well in the 'glow in the dark' territory. Human's lethal dose is 3..5 Sievert], and cells could start actually responding to count of events per time. (It is indeed well documented that cells do exhibit defene response at doses approaching 1 Sievert. The response (cell division arrest) is in no way generally beneficial (if your cells stop dividing, you'll die when your existing cells wear out), but you might survive otherwise lethal dose if cells are not dividing)

Conclusions: The linear no threshold model is based upon understanding that cells respond to ionizing radiation in probabilistic way; the linearity does not come from any simplified assumption about organism or cellular machinery, but rather from how statistics and probabilities work. When you increase dose ten times over background, you do not increase dose to any cells by ten times. You're increasing the very small population of cells which suffer an ionization event in the nucleus, ten times, thus increasing ten times the population of cells that can turn cancerous. (actually, worse than that. You're increasing hundred times the population of cells which suffer two ionization events, and thousand times population which suffers triple ionization event. Quadratic or cubic dose response effect has not been observed, though. There's a lot of other sources of DNA damage besides radiation)

But what's about multiple cells, you might ask? Immune system and whatnot? Well, this is pretty much covered by evolutionary objection above. Try imagine evolved organism that would somehow measure level of radiation by monitoring a lot of cells, just to handicap itself when the level of radiation is at or below natural background - and 'unhandicap' itself on the level of say 10x natural background (which is still very low and not life threatening, but is also very unusual in nature).
Makes no sense whatsoever. That's no strawman; that's what it takes for organism to exhibit effect of radiation hormesis. Barring any possibility of direct beneficial effect, the 'beneficial response' to a stimulus is equivalent to detrimental handicap in absence of stimulus.

Furthermore, hormesis is just bad science. Studies are fraudulent - consisting of comparisons between populations without control for the age group and smoking. As typical in scientific fraud, research conclusions focus entirely on the non-scientific aspects such as safety policies, entirely ignoring the scientific implications (if the response is not linear, then you have to throw entire concept of dose out of the window. It is only the linear no threshold response model under which all kinds of ionizing radiation are equivalent (up to the scaling factor)). To put it very bluntly, there's all reasons to think that hormesis proponents are not merely mistaken, but are actively lying. A genuinely mistaken scientist explores the scientific consequences of his erroneous research. A fraudster, on other hand, focuses solely on promoting the policy changes which he wants to enact through his fraud, and shies away from the scientific implications of his research; for the science is interlinked, and scientific implications of fraudulent research would contradict a lot of other, seemingly unrelated experiments and knowledge.