This paper in Nature Reviews Cancer is getting more attention in the popular press than most papers in that journal manage. Titled "Cancer: an old disease, a new disease or something in between?", it goes over the archaeological evidence for cancer rates in ancient populations, and goes on to speculate whether the incidence of the disease is higher under modern conditions.
I'd be interested in knowing that, too, but the problem seems to be that there's not much evidence one way or another. The authors concentrate on the evidence that can be found in bone samples, since these are naturally the most numerous, but it seems to be quite hard to get any meaningful histology data from ancient bone tissue. As for other tissue, the Egyptian record is probably the most statistically robust, thanks to deliberate mummification and the desert conditions, but even that isn't too definitive. The Greeks definitely described metastatic tumors, though (and in fact, gave us our name for the disease).
Still, they believe that the archaeological record indicates a smaller incidence of cancer than you'd expect, although given the long list of confounding factors they present, I'm not sure how sturdy that result is. One of the biggest of those is the shorter life expectancies in ancient populations, and it's not easy to get around that one. As the authors themselves point out, working-class ancient Egyptians seem to have mostly died at ages between 25 and 30 (!), and there aren't many forms of cancer that would be expected to show up well under those demographic conditions. (Osteosarcoma is the main tumor type the authors look for as being not so age-dependent).
The paper itself is fairly calm about its conclusions:
Despite the fact that other explanations, such as inadequate techniques of disease diagnosis, cannot be ruled out, the rarity of malignancies in antiquity is strongly suggested by the available palaeopathological and literary evidence. This might be related to the prevalence of carcinogens in modern societies.
But the press reports (based, I think, partly on further statements from the authors) haven't been. "Cancer Is A Modern Disease", "No Cancer In Ancient Times" go the headlines. (Go tell that last one to the ancient Greeks). And it's impossible to deny the environmental causes of some cancers - I'll bet that lung cancer rates prior to the introduction of tobacco into the Old World were pretty low, for example. Repeated exposure to some industrial chemicals (benzene and benzidine, right off the top of my head) are most definitely linked to increased risk of particular tumor types.
So in that way, modern cancer incidence probably is higher, at least for specific forms of the disease. But (as mentioned above) the single biggest factor is surely our longer lives. Eventually, some cells are going to hit on the wrong combination of mutations if you just give them enough time. And the widely reported statement from Professor Davids, one of the paper's authors, that "There is nothing in the natural environment that causes cancer", is flat-out wrong. What about UV light from the sun? Aflatoxins from molds? Phorbol esters in traditional herbal recipes?
That statement strongly suggests a habit of mind that I think has to be guarded against: the "Garden of Eden" effect. That's the belief, widely held in one form or another, that there was a time - long ago - when people were in harmony with nature, ate pure, wholesome natural foods (the kind that we were meant to eat), and didn't have all the horrible problems that we have in these degenerate modern times. (You can see a lot of Rousseau in there, too, what with all that Noble Savage, corrupted-by-modern-society stuff).
This 1990 article (PDF) by Bruce Ames and Lois Gold, "Misconceptions on Pollution and the Causes of Cancer" is a useful corrective to the idea that modern environments cause all cancers. You'll have to guard yourselves, though, against the prelapsarian Golden Age fallacy. It's everywhere.